Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions

• Main Authors: Chalykh, Oleg (Author), Etingof, Pavel I. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Elsevier, 2014-05-05T13:05:53Z.
• Subjects: Article
• Online Access: Get fulltext

Author Manuscript 27 Feb 2013
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.
National Science Foundation (U.S.) (Grant DMS-1000113)