Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions
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Etingof_Othogonality relations.pdf
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Author(s)
Chalykh, Oleg
Etingof, Pavel I.
Date Issued
March 2013
Journal
Advances in Mathematics
Publisher
Elsevier
Citation
Chalykh, Oleg, and Pavel Etingof. “Orthogonality relations and Cherednik identities for multivariable Baker–Akhiezer functions.” Advances in Mathematics 238 (May 2013): 246-289.
Version
Author's final manuscript
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.
Description
Author Manuscript 27 Feb 2013
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.aim.2013.01.010
