A Commutative Family of Integral Transformations and Basic Hypergeometric Series. II. Eigenfunctions and Quasi-Eigenfunctions
| dc.creator | Shiraishi, Jun'ichi | |
| dc.date | 2005-02-11 | |
| dc.date | 2005-05-12 | |
| dc.date.accessioned | 2026-07-07T05:16:53Z | |
| dc.date.available | 2026-07-07T05:16:53Z | |
| dc.description | A series of conjectures is obtained as further investigation of the integral transformation I(alpha) introduced in the previous paper. A Macdonald-type difference operator D is introduced. It is conjectured that D and I(alpha) are commutative with each other. Studying the series for the eigenfunctions under termination conditions, it is observed that a deformed Weyl group action appears as a hidden symmetry. An infinite product formula for the eigenfunction is found for a spacial case of parameters. A one parameter family of hypergeometric-type series F(alpha) is introduced. The series F(alpha) is caracterized by a covariant transformation property I(alpha q^{-1} t) F(alpha)=F(alpha q^{-1} t) and a certain initial condition given at alpha=t^{1/2}. We call F(alpha) the `quasi-eigenfunction' for short. A class of infinite product-type expressions are conjectured for F(alpha) at the special points alpha=-t^{1/2}, alpha=q, alpha=pm q^{1/2}t^{1/2}, and alpha=pm q^{ell}t^{1/2} (ell=1,2,3,cdots). | |
| dc.description | Basic parameters replaced: q -> t, and p^{1/2} -> q | |
| dc.identifier | https://arxiv.org/abs/math/0502228 | |
| dc.identifier | http://arxiv.org/abs/math/0502228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74153 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 33D15, 81R50 | |
| dc.title | A Commutative Family of Integral Transformations and Basic Hypergeometric Series. II. Eigenfunctions and Quasi-Eigenfunctions | |
| dc.type | text |