Askey-Wilson functions and quantum groups
| dc.creator | Stokman, Jasper V. | |
| dc.date | 2003-01-28 | |
| dc.date.accessioned | 2026-07-07T04:54:44Z | |
| dc.date.available | 2026-07-07T04:54:44Z | |
| dc.description | Eigenfunctions of the Askey-Wilson second order $q$-difference operator for $0<q<1$ and $|q|=1$ are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra $U_q(sl(2,\mathbb{C}))$. The eigenfunctions are in integral form and may be viewed as analogues of Euler's integral representation for Gauss' hypergeometric series. We show that for $0<q<1$ the resulting eigenfunction can be rewritten as a very-well-poised ${}_8ϕ_7$-series, and reduces for special parameter values to a natural elliptic analogue of the cosine kernel. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301330 | |
| dc.identifier | http://arxiv.org/abs/math/0301330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66374 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Representation Theory | |
| dc.title | Askey-Wilson functions and quantum groups | |
| dc.type | text |