Baxter operators in Ruijsenaars hyperbolic system II. Bispectral wave functions
Mathematical Physics
2023-08-30 v3 High Energy Physics - Theory
math.MP
Quantum Algebra
Representation Theory
Abstract
In the previous paper we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work we show that the wave functions of the quantum system found by M. Halln\"as and S. Ruijsenaars also diagonalize Baxter operators. Using this property we prove the conjectured duality relation for the wave function. As a corollary, we show that the wave function solves bispectral problems for pairs of dual Macdonald and Baxter operators. Besides, we prove the conjectured symmetry of the wave function with respect to spectral variables and obtain new integral representation for it.
Cite
@article{arxiv.2303.06382,
title = {Baxter operators in Ruijsenaars hyperbolic system II. Bispectral wave functions},
author = {N. Belousov and S. Derkachov and S. Kharchev and S. Khoroshkin},
journal= {arXiv preprint arXiv:2303.06382},
year = {2023}
}