Lie algebras and recurrence relations III:q-analogs and quantized algebras (original) (raw)

q-Analogs of the basic structures discussed in 'Lie Algebras and Recurrence Relations I' are presented. The q-Heisenberg-Weyl (qHW) and qsl(2) algebras are discussed in detail. Presently it is known that such structures are very closely tied in with the theory of quantum groups. Among other topics, coherent state representations and their interpretations as q-identities for q-Hermite and AI-Salam-Chihara (q-Meixner) polynomials are discussed. A discussion of Clebsch-Gordan coefficients for a qsu(2)type algebra is presented.