Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666076 | Advances in Mathematics | 2013 | 44 Pages |
Abstract
We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new quantum integrable models of Macdonald–Ruijsenaars type.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Oleg Chalykh, Pavel Etingof,