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Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions

Chalykh, O and Etingof, P (2012) Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions. Advances in Mathematics. ISSN 0001-8708 (Submitted)

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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 introduce more general twisted BA functions and obtain for them identities of Cherednik type. This leads to an implicit construction of new quantum integrable models of Macdonald-Ruijsenaars type. Our approach does not require Hecke algebras and therefore is applicable to deformed root systems. As an example, we consider the deformed root system R=A_n(m), which leads us to an explicit evaluation of a new integral and a sum of Cherednik-Macdonald-Mehta type.

Item Type: Article
Copyright, Publisher and Additional Information: © 2012, Elsevier. This is an author produced version of a paper accepted for publication in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 02 Jul 2012 10:41
Last Modified: 07 Jun 2014 02:36
Status: Submitted
Publisher: Elsevier
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/74388

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