Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians

Simple item page
dc.creatorDijkhuizen, Mathijs S.
dc.creatorStokman, Jasper V.
dc.date1998-06-23
dc.date.accessioned2026-07-07T05:25:09Z
dc.date.available2026-07-07T05:25:09Z
dc.descriptionThe quantum complex Grassmannian U_q/K_q of rank l is the quotient of the quantum unitary group U_q=U_q(n) by the quantum subgroup K_q=U_q(n-l)xU_q(l). We show that (U_q,K_q) is a quantum Gelfand pair and we express the zonal spherical functions, i.e. K_q-biinvariant matrix coefficients of finite- dimensional irreducible representations of U_q, as multivariable little q-Jacobi polynomials depending on one discrete parameter. Another type of biinvariant matrix coefficients is identified as multivariable big q-Jacobi polynomials. The proof is based on earlier results by Noumi, Sugitani and the first author relating Koornwinder polynomials to a one-parameter family of quantum complex Grassmannians, and certain limit transitions from Koornwinder polynomials to multivariable big and little q-Jacobi polynomials studied by Koornwinder and the second author.
dc.description39 pages, no figures, Latex2e
dc.identifierhttps://arxiv.org/abs/math/9806123
dc.identifierhttp://arxiv.org/abs/math/9806123
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77077
dc.subjectQuantum Algebra
dc.subject33D80;33D45
dc.titleSome limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
dc.typetext

Files

Collections

arXiv