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Papers by Charles Dunkl

Research paper thumbnail of A Family of Crouzeix-Raviart Finite Elements in 3D

arXiv (Cornell University), Mar 9, 2017

Research paper thumbnail of A Laguerre Polynomial Orthogonality and the Hydrogen Atom

arXiv (Cornell University), Nov 13, 2000

The radial part of the wave function of an electron in a Coulomb potential is the product of a La... more The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis an analogous strange orthogonality is obtained for Meixner polynomials.

Research paper thumbnail of Hook-lengths and pairs of compositions

Journal of Computational and Applied Mathematics, Feb 1, 2007

Research paper thumbnail of The Sums of a Double Hypergeometric Series and of the First m+1 Terms of 3F2(a,b,c;(a+b+1)/2,2c;1) when c = -m is a Negative Integer

arXiv (Cornell University), Dec 12, 2014

Research paper thumbnail of Bounded Projections on Fourier-Stieltjes Transforms

Proceedings of the American Mathematical Society, 1972

Research paper thumbnail of Factorizations of Symmetric Macdonald Polynomials

Research paper thumbnail of Symmetric functions and<i>B<sub>N</sub></i>-invariant spherical harmonics

Journal of physics, Nov 19, 2002

Research paper thumbnail of Operators and harmonic analysis on the sphere

Transactions of the American Mathematical Society, 1966

Research paper thumbnail of Products of Beta distributed random variables

arXiv (Cornell University), Apr 24, 2013

Research paper thumbnail of An Intertwining Operator for the Group B2

arXiv (Cornell University), Jul 31, 2006

Research paper thumbnail of Some Singular Vector-Valued Jack and Macdonald Polynomials

Research paper thumbnail of Whole and Half Generalized Two-Qubit Hilbert-Schmidt Separability Probabilities

arXiv (Cornell University), Apr 7, 2014

Research paper thumbnail of Some Rarita-Schwinger Operators

arXiv (Cornell University), Feb 6, 2011

Research paper thumbnail of Dunkl Operators and Related Special Functions

Cambridge University Press eBooks, Oct 15, 2020

Research paper thumbnail of Integrals of polynomials associated with tableaux and the Garsia-Haiman conjecture

Mathematische Zeitschrift, Jul 1, 1998

Research paper thumbnail of Separability probability formulas and their proofs for generalized two-qubit X-matrices endowed with Hilbert–Schmidt and induced measures

Random matrices : theory and applications, Oct 1, 2015

Research paper thumbnail of Symmetric and Antisymmetric Vector-valued Jack Polynomials

arXiv (Cornell University), Jan 25, 2010

Polynomials with values in an irreducible module of the symmetric group can be given the structur... more Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the standard module. Such polynomials of minimum degree have norms which involve hook-lengths and generalize the norm of the alternating polynomial. 0. Suppose τ is a partition of N , that is, |τ | = N ; then there is an associated

Research paper thumbnail of Generalized Jack polynomials and the representation theory of rational Cherednik algebras

arXiv (Cornell University), Feb 24, 2010

Research paper thumbnail of A positive-definite inner product for vector-valued Macdonald polynomials

arXiv (Cornell University), Aug 15, 2018

Research paper thumbnail of The smallest singular values of the icosahedral group

arXiv (Cornell University), Sep 6, 2018

Research paper thumbnail of A Family of Crouzeix-Raviart Finite Elements in 3D

arXiv (Cornell University), Mar 9, 2017

Research paper thumbnail of A Laguerre Polynomial Orthogonality and the Hydrogen Atom

arXiv (Cornell University), Nov 13, 2000

The radial part of the wave function of an electron in a Coulomb potential is the product of a La... more The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis an analogous strange orthogonality is obtained for Meixner polynomials.

Research paper thumbnail of Hook-lengths and pairs of compositions

Journal of Computational and Applied Mathematics, Feb 1, 2007

Research paper thumbnail of The Sums of a Double Hypergeometric Series and of the First m+1 Terms of 3F2(a,b,c;(a+b+1)/2,2c;1) when c = -m is a Negative Integer

arXiv (Cornell University), Dec 12, 2014

Research paper thumbnail of Bounded Projections on Fourier-Stieltjes Transforms

Proceedings of the American Mathematical Society, 1972

Research paper thumbnail of Factorizations of Symmetric Macdonald Polynomials

Research paper thumbnail of Symmetric functions and<i>B<sub>N</sub></i>-invariant spherical harmonics

Journal of physics, Nov 19, 2002

Research paper thumbnail of Operators and harmonic analysis on the sphere

Transactions of the American Mathematical Society, 1966

Research paper thumbnail of Products of Beta distributed random variables

arXiv (Cornell University), Apr 24, 2013

Research paper thumbnail of An Intertwining Operator for the Group B2

arXiv (Cornell University), Jul 31, 2006

Research paper thumbnail of Some Singular Vector-Valued Jack and Macdonald Polynomials

Research paper thumbnail of Whole and Half Generalized Two-Qubit Hilbert-Schmidt Separability Probabilities

arXiv (Cornell University), Apr 7, 2014

Research paper thumbnail of Some Rarita-Schwinger Operators

arXiv (Cornell University), Feb 6, 2011

Research paper thumbnail of Dunkl Operators and Related Special Functions

Cambridge University Press eBooks, Oct 15, 2020

Research paper thumbnail of Integrals of polynomials associated with tableaux and the Garsia-Haiman conjecture

Mathematische Zeitschrift, Jul 1, 1998

Research paper thumbnail of Separability probability formulas and their proofs for generalized two-qubit X-matrices endowed with Hilbert–Schmidt and induced measures

Random matrices : theory and applications, Oct 1, 2015

Research paper thumbnail of Symmetric and Antisymmetric Vector-valued Jack Polynomials

arXiv (Cornell University), Jan 25, 2010

Polynomials with values in an irreducible module of the symmetric group can be given the structur... more Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the standard module. Such polynomials of minimum degree have norms which involve hook-lengths and generalize the norm of the alternating polynomial. 0. Suppose τ is a partition of N , that is, |τ | = N ; then there is an associated

Research paper thumbnail of Generalized Jack polynomials and the representation theory of rational Cherednik algebras

arXiv (Cornell University), Feb 24, 2010

Research paper thumbnail of A positive-definite inner product for vector-valued Macdonald polynomials

arXiv (Cornell University), Aug 15, 2018

Research paper thumbnail of The smallest singular values of the icosahedral group

arXiv (Cornell University), Sep 6, 2018

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