Владимир Алексеевич Стукопин | Moscow Institute of Physics and Technology (original) (raw)

Papers by Владимир Алексеевич Стукопин

Research paper thumbnail of On Distribution of Eigen Values of Toeplitz Matrices with Hartwig-Fisher Symbol

Вестник Донского государственного технического университета, 2018

Toeplitz matrices with Hartwig-Fisher symbol are investigated. The extension of Szego theorem for... more Toeplitz matrices with Hartwig-Fisher symbol are investigated. The extension of Szego theorem for normal Toeplitz matrices with complex-valued symbol from L? space on the unit circle is formulated and proved.

Research paper thumbnail of Yangians of Lie superalgebras of type A ( m, n )

Funct Anal Appl Engl Tr, 1994

Research paper thumbnail of Yangian of the Strange Lie Superalgebra of $ boldsymbol{Q_{n-1}}$ Type, Drinfel'd Approach

Symmetry Integr Geom, 2007

Research paper thumbnail of Homotopy classification of families of Noetherian singular operators with piecewise continuous coefficients on a composite contour

Research paper thumbnail of The Yangian of the strange Lie superalgebra and its quantum double

Theoretical and Mathematical Physics, 2013

We construct the Yangian of the strange Lie superalgebra as a particular case of the general cons... more We construct the Yangian of the strange Lie superalgebra as a particular case of the general construction of a twisted Yangian. We describe a Poincaré-Birkhoff-Witt basis of the Yangian of the type-Qn Lie superalgebra and construct the quantum double of the Yangian of the type-Q2 strange Lie superalgebra.

Research paper thumbnail of Yangian of the Strange Lie Superalgebra of Q n-1 Type, Drinfel'd Approach

Symmetry, Integrability and Geometry: Methods and Applications, 2007

The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current sys... more The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current system generators and defining relations are described.

Research paper thumbnail of The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA 1 (1)

Letters in Mathematical Physics, 1993

The universal quantum R-matrix is obtained in the case of the affine Kac Moody Lie algebra sl(2).

Research paper thumbnail of On representations of Yangian of Lie SuperalgebraA(n,n) type

Journal of Physics: Conference Series, 2013

The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type... more The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type is described in terms of Drinfel'd polynomials. The necessarily and sufficient conditions of finite-dimensionality of irreducible representation are formulated and proved. The Poincare-Birkoff-Witt theorem for Yangian of A(n, n) Lie Superalgebra is proved also. 0 This work is partially supported by Federal Program "Scientific and scientific-educational personnel of innovative Russia event 1.2.2 (contract number P116) and by Federal Program "Scientific and scientific-educational personnel of innovative Russia"(agreement № 14.A18.

Research paper thumbnail of The quantum double of the Yangian of the Lie superalgebra A(m, n) and computation of the universal R-matrix

Journal of Mathematical Sciences, 2007

The Yangian double DY (A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generato... more The Yangian double DY (A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generators and defining relations. We prove the triangular decomposition for Yangian Y (A(m, n)) and its quantum double DY (A(m, n)) as a corollary of the PBW theorem. We introduce normally ordered bases in the Yangian and its dual Hopf superalgebra in the quantum double. We calculate the pairing formulas between the elements of these bases. We obtain the formula for the universal R-matrix of the Yangian double. The formula for the universal R-matrix of the Yangian, which was introduced by V. Drinfel'd, is also obtained.

Research paper thumbnail of Yangian Double of Strange Lie Superalgebra Qn and its Central Extension: Basic results and formulas for Universal R-matrix

The Yangian Y (Qn) of strange Lie superalgebra of Qn type, its quantum double DY (Qn) and the cen... more The Yangian Y (Qn) of strange Lie superalgebra of Qn type, its quantum double DY (Qn) and the central extension of quantum double are described as a results of quantization of twisted current Lie superbialgebras of polyno- mial currents, of Laurant currents and its central extension, correspondingly. Two systems of generators and defining relations for Yangian are introduced. Equivalence of this systems of generators and defining relations is proved. PBW theorem is formulated and proved. The double of Yangian and its central extension are described in terms of generators and defining rela- tions. Formulas for universal R-matrix for double of Yangian and its central extension are computed. It is well-known that Lie superalgebras of classical type divided on two

Research paper thumbnail of Asymptotics of eigenvalues of symmetric Toeplitz band matrices

Linear Algebra and its Applications, 2015

ABSTRACT In this paper we obtain uniform asymptotic formulas for all eigenvalues of symmetric Toe... more ABSTRACT In this paper we obtain uniform asymptotic formulas for all eigenvalues of symmetric Toeplitz band matrices of large dimension. The entries of the matrices are assumed to be complex, that is, the matrices need not necessarily be self-adjoint. The formulas presented allow a detailed study of the structure of the eigenvalues and of their location in the complex plane, and to build an efficient algorithm for finding their numerical values for matrices of medium and high dimension.

Research paper thumbnail of Аффинный суперянгиан и квантовый группоид Вейля

Teoreticheskaya i Matematicheskaya Fizika

Определены две реализации аффинного суперянгиана Yhbar(widehatsl(m∣n))Y_{\hbar}(\widehat{sl}(m|n))Yhbar(widehatsl(m∣n)) специальной линей... more Определены две реализации аффинного суперянгиана Yhbar(widehatsl(m∣n))Y_{\hbar}(\widehat{sl}(m|n))Yhbar(widehatsl(m∣n)) специальной линейной супералгебры Каца-Муди widehatsl(m∣n)\widehat{sl}(m|n)widehatsl(m∣n) для произвольной системы простых корней: в терминах "минималистской" системы образующих и новой системы образующих Дринфельда. Построен изоморфизм между этими двумя реализациями суперянгиана в случае фиксированной системы простых корней. Рассмотрен группоид Вейля, определен его квантовый аналог и задано его действие на суперянгианах, определяемых системами простых корней. Показано, что действие квантового группоида Вейля индуцирует изоморфизмы между суперянгианами, определяемыми разными системами простых корней.

Research paper thumbnail of Квазитреугольные структуры на суперянгиане и квантовой петлевой супералгебре и разностные уравнения

Teoreticheskaya i Matematicheskaya Fizika

В рамках подхода Толедано-Ларедо и Гаутама рассматриваются структуры тензорных категорий на анало... more В рамках подхода Толедано-Ларедо и Гаутама рассматриваются структуры тензорных категорий на аналогах категории mathfrakO\mathfrak{O}mathfrakO для представлений суперянгиана Yhbar(A(m,n))Y_{\hbar}(A(m,n))Yhbar(A(m,n)) специальной линейной супералгебры Ли и квантовой петлевой супералгебры Uq(LA(m,n))U_q(LA(m,n))Uq(LA(m,n)), исследуется связь между ними. Основным результатом работы является конструкция изоморфизма в категории супералгебр Хопфа между пополнениями суперянгиана и квантовой петлевой супералгебры, наделенными так называемыми дринфельдовскими коумножениями. Формулируется теорема об эквивалентности тензорных категорий модулей суперянгиана и квантовой петлевой супералгебры, усиливающая предыдущий результат. Также описывается связь между квазитреугольными структурами и абелевыми разностными уравнениями, которые определяются абелевыми частями универсальных RRR-матриц.

Research paper thumbnail of On Classification of Yangian Irreducible Representations of Lie Superalgebra SL (1, 2)

Вестник Донского государственного технического университета, 2018

The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra ... more The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra sl(1,2) – Hopf superalgebra is obtained. The classification is of great use in modern theoretical and mathematical physics. Some feasible applications of this result in mathematical physics are offered.

Research paper thumbnail of О связи категорий представлений суперянгиана специальной линейной супералгебры Ли и квантовой петлевой супералгебры

Teoreticheskaya i Matematicheskaya Fizika, 2020

С использованием подхода Гаутама и Толедано-Ларедо вводятся аналоги категории mathfrakO\mathfrak OmathfrakO для п... more С использованием подхода Гаутама и Толедано-Ларедо вводятся аналоги категории mathfrakO\mathfrak OmathfrakO для представлений янгиана Yhbar(A(m,n))Y_\hbar(A(m,n))Yhbar(A(m,n)) специальной линейной супералгебры Ли и квантовой петлевой супералгебры Uq(LA(m,n))U_q(LA(m,n))Uq(LA(m,n)). Исследуется связь между ними и сформулирована гипотеза об эквивалентности этих категорий.

Research paper thumbnail of Representations Theory and Doubles of Yangians of Classical Lie Superalgebras

Asymptotic Combinatorics with Application to Mathematical Physics, 2002

Some basic results of the theory of Yangians of Lie superalgebras are described. The Yangian of a... more Some basic results of the theory of Yangians of Lie superalgebras are described. The Yangian of a classical Lie superalgebra is described as a result of quantization of the Lie superbialgebra of polynomial loops. Two systems of generators and defining relations are introduced, and their equivalence is proved. The PBW theorem for the Yangians of classical Lie superalgebras is formulated and proved. All irreducible finite-dimensional representations of the Yangians of Lie superalgebras of type A(m,n) are described in terms of Drinfel’d polynomials. A notion of the double of a Yangian and a formula for the universal R-matrix for the double of a Yangian are discussed for the Yangian of a Lie superalgebra of type A(m,n).

Research paper thumbnail of Drinfeld Yangian of the queer Lie superalgebra sq 1

Journal of Physics: Conference Series, 2019

Drinfeld Yangian of a queer Lie superalgebra sq1 is defined as the quantization of a Lie bisupere... more Drinfeld Yangian of a queer Lie superalgebra sq1 is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the case Lie superalgebra sq1 that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev-Reshetikhin-Takhtadzhjan approach, are isomorphic.

Research paper thumbnail of Geometric realization of electronic elections based on threshold secret sharing

Vestnik of Don State Technical University, 2018

Research paper thumbnail of Representations of the Yangian of a Lie superalgebra of type $ A(m,n)$

Izvestiya: Mathematics, 2013

Atomic and molecular processes relevant to the volumetric recombination phenomena were investigat... more Atomic and molecular processes relevant to the volumetric recombination phenomena were investigated in a linear divertor plasma simulator MAP-11. Volumetric recombination is induced in He plasma by puffing of He or Hz. In the He puffing case, the reduction of the ion flux is dominated by the electron-ion recombination. In the Hz puffing case, however, it is dominated by the molecule-assisted recombination (MAR), which is characterized by the disappearance of the Helium Rydberg spectra and by the existence of the hydrogen negative ions. Current achievement and the future prospect are described.

Research paper thumbnail of The index of families of Noether singular and bisingular operators with piecewise continuous coefficients on composite contours

Research paper thumbnail of On Distribution of Eigen Values of Toeplitz Matrices with Hartwig-Fisher Symbol

Вестник Донского государственного технического университета, 2018

Toeplitz matrices with Hartwig-Fisher symbol are investigated. The extension of Szego theorem for... more Toeplitz matrices with Hartwig-Fisher symbol are investigated. The extension of Szego theorem for normal Toeplitz matrices with complex-valued symbol from L? space on the unit circle is formulated and proved.

Research paper thumbnail of Yangians of Lie superalgebras of type A ( m, n )

Funct Anal Appl Engl Tr, 1994

Research paper thumbnail of Yangian of the Strange Lie Superalgebra of $ boldsymbol{Q_{n-1}}$ Type, Drinfel'd Approach

Symmetry Integr Geom, 2007

Research paper thumbnail of Homotopy classification of families of Noetherian singular operators with piecewise continuous coefficients on a composite contour

Research paper thumbnail of The Yangian of the strange Lie superalgebra and its quantum double

Theoretical and Mathematical Physics, 2013

We construct the Yangian of the strange Lie superalgebra as a particular case of the general cons... more We construct the Yangian of the strange Lie superalgebra as a particular case of the general construction of a twisted Yangian. We describe a Poincaré-Birkhoff-Witt basis of the Yangian of the type-Qn Lie superalgebra and construct the quantum double of the Yangian of the type-Q2 strange Lie superalgebra.

Research paper thumbnail of Yangian of the Strange Lie Superalgebra of Q n-1 Type, Drinfel'd Approach

Symmetry, Integrability and Geometry: Methods and Applications, 2007

The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current sys... more The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current system generators and defining relations are described.

Research paper thumbnail of The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA 1 (1)

Letters in Mathematical Physics, 1993

The universal quantum R-matrix is obtained in the case of the affine Kac Moody Lie algebra sl(2).

Research paper thumbnail of On representations of Yangian of Lie SuperalgebraA(n,n) type

Journal of Physics: Conference Series, 2013

The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type... more The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type is described in terms of Drinfel'd polynomials. The necessarily and sufficient conditions of finite-dimensionality of irreducible representation are formulated and proved. The Poincare-Birkoff-Witt theorem for Yangian of A(n, n) Lie Superalgebra is proved also. 0 This work is partially supported by Federal Program "Scientific and scientific-educational personnel of innovative Russia event 1.2.2 (contract number P116) and by Federal Program "Scientific and scientific-educational personnel of innovative Russia"(agreement № 14.A18.

Research paper thumbnail of The quantum double of the Yangian of the Lie superalgebra A(m, n) and computation of the universal R-matrix

Journal of Mathematical Sciences, 2007

The Yangian double DY (A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generato... more The Yangian double DY (A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generators and defining relations. We prove the triangular decomposition for Yangian Y (A(m, n)) and its quantum double DY (A(m, n)) as a corollary of the PBW theorem. We introduce normally ordered bases in the Yangian and its dual Hopf superalgebra in the quantum double. We calculate the pairing formulas between the elements of these bases. We obtain the formula for the universal R-matrix of the Yangian double. The formula for the universal R-matrix of the Yangian, which was introduced by V. Drinfel'd, is also obtained.

Research paper thumbnail of Yangian Double of Strange Lie Superalgebra Qn and its Central Extension: Basic results and formulas for Universal R-matrix

The Yangian Y (Qn) of strange Lie superalgebra of Qn type, its quantum double DY (Qn) and the cen... more The Yangian Y (Qn) of strange Lie superalgebra of Qn type, its quantum double DY (Qn) and the central extension of quantum double are described as a results of quantization of twisted current Lie superbialgebras of polyno- mial currents, of Laurant currents and its central extension, correspondingly. Two systems of generators and defining relations for Yangian are introduced. Equivalence of this systems of generators and defining relations is proved. PBW theorem is formulated and proved. The double of Yangian and its central extension are described in terms of generators and defining rela- tions. Formulas for universal R-matrix for double of Yangian and its central extension are computed. It is well-known that Lie superalgebras of classical type divided on two

Research paper thumbnail of Asymptotics of eigenvalues of symmetric Toeplitz band matrices

Linear Algebra and its Applications, 2015

ABSTRACT In this paper we obtain uniform asymptotic formulas for all eigenvalues of symmetric Toe... more ABSTRACT In this paper we obtain uniform asymptotic formulas for all eigenvalues of symmetric Toeplitz band matrices of large dimension. The entries of the matrices are assumed to be complex, that is, the matrices need not necessarily be self-adjoint. The formulas presented allow a detailed study of the structure of the eigenvalues and of their location in the complex plane, and to build an efficient algorithm for finding their numerical values for matrices of medium and high dimension.

Research paper thumbnail of Аффинный суперянгиан и квантовый группоид Вейля

Teoreticheskaya i Matematicheskaya Fizika

Определены две реализации аффинного суперянгиана Yhbar(widehatsl(m∣n))Y_{\hbar}(\widehat{sl}(m|n))Yhbar(widehatsl(m∣n)) специальной линей... more Определены две реализации аффинного суперянгиана Yhbar(widehatsl(m∣n))Y_{\hbar}(\widehat{sl}(m|n))Yhbar(widehatsl(m∣n)) специальной линейной супералгебры Каца-Муди widehatsl(m∣n)\widehat{sl}(m|n)widehatsl(m∣n) для произвольной системы простых корней: в терминах "минималистской" системы образующих и новой системы образующих Дринфельда. Построен изоморфизм между этими двумя реализациями суперянгиана в случае фиксированной системы простых корней. Рассмотрен группоид Вейля, определен его квантовый аналог и задано его действие на суперянгианах, определяемых системами простых корней. Показано, что действие квантового группоида Вейля индуцирует изоморфизмы между суперянгианами, определяемыми разными системами простых корней.

Research paper thumbnail of Квазитреугольные структуры на суперянгиане и квантовой петлевой супералгебре и разностные уравнения

Teoreticheskaya i Matematicheskaya Fizika

В рамках подхода Толедано-Ларедо и Гаутама рассматриваются структуры тензорных категорий на анало... more В рамках подхода Толедано-Ларедо и Гаутама рассматриваются структуры тензорных категорий на аналогах категории mathfrakO\mathfrak{O}mathfrakO для представлений суперянгиана Yhbar(A(m,n))Y_{\hbar}(A(m,n))Yhbar(A(m,n)) специальной линейной супералгебры Ли и квантовой петлевой супералгебры Uq(LA(m,n))U_q(LA(m,n))Uq(LA(m,n)), исследуется связь между ними. Основным результатом работы является конструкция изоморфизма в категории супералгебр Хопфа между пополнениями суперянгиана и квантовой петлевой супералгебры, наделенными так называемыми дринфельдовскими коумножениями. Формулируется теорема об эквивалентности тензорных категорий модулей суперянгиана и квантовой петлевой супералгебры, усиливающая предыдущий результат. Также описывается связь между квазитреугольными структурами и абелевыми разностными уравнениями, которые определяются абелевыми частями универсальных RRR-матриц.

Research paper thumbnail of On Classification of Yangian Irreducible Representations of Lie Superalgebra SL (1, 2)

Вестник Донского государственного технического университета, 2018

The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra ... more The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra sl(1,2) – Hopf superalgebra is obtained. The classification is of great use in modern theoretical and mathematical physics. Some feasible applications of this result in mathematical physics are offered.

Research paper thumbnail of О связи категорий представлений суперянгиана специальной линейной супералгебры Ли и квантовой петлевой супералгебры

Teoreticheskaya i Matematicheskaya Fizika, 2020

С использованием подхода Гаутама и Толедано-Ларедо вводятся аналоги категории mathfrakO\mathfrak OmathfrakO для п... more С использованием подхода Гаутама и Толедано-Ларедо вводятся аналоги категории mathfrakO\mathfrak OmathfrakO для представлений янгиана Yhbar(A(m,n))Y_\hbar(A(m,n))Yhbar(A(m,n)) специальной линейной супералгебры Ли и квантовой петлевой супералгебры Uq(LA(m,n))U_q(LA(m,n))Uq(LA(m,n)). Исследуется связь между ними и сформулирована гипотеза об эквивалентности этих категорий.

Research paper thumbnail of Representations Theory and Doubles of Yangians of Classical Lie Superalgebras

Asymptotic Combinatorics with Application to Mathematical Physics, 2002

Some basic results of the theory of Yangians of Lie superalgebras are described. The Yangian of a... more Some basic results of the theory of Yangians of Lie superalgebras are described. The Yangian of a classical Lie superalgebra is described as a result of quantization of the Lie superbialgebra of polynomial loops. Two systems of generators and defining relations are introduced, and their equivalence is proved. The PBW theorem for the Yangians of classical Lie superalgebras is formulated and proved. All irreducible finite-dimensional representations of the Yangians of Lie superalgebras of type A(m,n) are described in terms of Drinfel’d polynomials. A notion of the double of a Yangian and a formula for the universal R-matrix for the double of a Yangian are discussed for the Yangian of a Lie superalgebra of type A(m,n).

Research paper thumbnail of Drinfeld Yangian of the queer Lie superalgebra sq 1

Journal of Physics: Conference Series, 2019

Drinfeld Yangian of a queer Lie superalgebra sq1 is defined as the quantization of a Lie bisupere... more Drinfeld Yangian of a queer Lie superalgebra sq1 is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the case Lie superalgebra sq1 that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev-Reshetikhin-Takhtadzhjan approach, are isomorphic.

Research paper thumbnail of Geometric realization of electronic elections based on threshold secret sharing

Vestnik of Don State Technical University, 2018

Research paper thumbnail of Representations of the Yangian of a Lie superalgebra of type $ A(m,n)$

Izvestiya: Mathematics, 2013

Atomic and molecular processes relevant to the volumetric recombination phenomena were investigat... more Atomic and molecular processes relevant to the volumetric recombination phenomena were investigated in a linear divertor plasma simulator MAP-11. Volumetric recombination is induced in He plasma by puffing of He or Hz. In the He puffing case, the reduction of the ion flux is dominated by the electron-ion recombination. In the Hz puffing case, however, it is dominated by the molecule-assisted recombination (MAR), which is characterized by the disappearance of the Helium Rydberg spectra and by the existence of the hydrogen negative ions. Current achievement and the future prospect are described.

Research paper thumbnail of The index of families of Noether singular and bisingular operators with piecewise continuous coefficients on composite contours