Orthogonality relations and Cherednik identities for multivariable\n Baker-Akhiezer functions

2011/11/02 by Oleg Chalykh, Pavel Etingof, Chalykh, Oleg +1 · 1 citation
Chemistry · Physics and Astronomy · Materials Science · #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Nonlinear Optical Materials Research

paper · pdf · doi:10.48550/arxiv.1111.0515

Abstract

We establish orthogonality relations for the Baker-Akhiezer (BA)\neigenfunctions of the Macdonald difference operators. We also obtain a version\nof Cherednik-Macdonald-Mehta integral for these functions. As a corollary, we\ngive a simple derivation of the norm identity and Cherednik-Macdonald-Mehta\nintegral for Macdonald polynomials. In the appendix written by the first\nauthor, we prove a summation formula for BA functions. We also consider more\ngeneral identities of Cherednik type, which we use to introduce and construct\nmore general, twisted BA functions. This leads to a construction of new quantum\nintegrable models of Macdonald-Ruijsenaars type.\n

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• Baker-Akhiezer specialisation of joint eigenfunctions for hyperbolic relativistic Calogero-Moser Hamiltonians
• Macdonald deformation of Vogel's universality and link hyperpolynomials

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