Whittaker limits of difference spherical functions
| dc.creator | Cherednik, Ivan | |
| dc.date | 2008-07-14 | |
| dc.date | 2009-04-24 | |
| dc.date.accessioned | 2026-07-07T13:07:31Z | |
| dc.date.available | 2026-07-07T13:07:31Z | |
| dc.description | We introduce the (global) q-Whittaker function as the limit at t=0 of the q,t-spherical function extending the symmetric Macdonald polynomials to arbitrary eigenvalues. The construction heavily depends on the technique of the q-Gaussians developed by the author (and Stokman in the non-reduced case). In this approach, the q-Whittaker function is given by a series convergent everywhere, a kind of generating function for multi-dimensional q-Hermite polynomials (closely related to the level 1 Demazure characters). One of the applications is a q-version of the Shintani- Casselman- Shalika formula, which appeared directly connected with q-Mehta- Macdonald identities in terms of the Jackson integrals. This formula generalizes that of type A due to Gerasimov et al. to arbitrary reduced root systems. At the end of the paper, we obtain a q,t-counterpart of the Harish-Chandra asymptotic formula for the spherical functions, including the Whittaker limit. | |
| dc.description | V2: a discussion of the one-dimensional case was added. V3: Jackson integration and growth estimates were added. V4: a q-variant of the Harish-Chandra asymptotic formula for spherical functions was added. V5: editing, some improvements, adding references. V6: General editing | |
| dc.identifier | https://arxiv.org/abs/0807.2155 | |
| dc.identifier | http://arxiv.org/abs/0807.2155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228114 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Whittaker limits of difference spherical functions | |
| dc.type | text |