A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials
| dc.creator | Dijkhuizen, M. S. | |
| dc.creator | Noumi, M. | |
| dc.date | 1996-05-13 | |
| dc.date.accessioned | 2026-07-07T09:16:57Z | |
| dc.date.available | 2026-07-07T09:16:57Z | |
| dc.description | We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with respect to the natural transitive U_q(n)-action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little q-Jacobi polynomials depending on one discrete parameter. | |
| dc.description | 31 pages, AMS-TeX 2.1, no figures | |
| dc.identifier | https://arxiv.org/abs/q-alg/9605017 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9605017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153540 | |
| dc.subject | Quantum Algebra | |
| dc.title | A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials | |
| dc.type | text |