Q-operators for the Ruijsenaars model
Mathematical Physics
2025-03-25 v1 Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
We prove that the Ruijsenaars model admits a one-parameter commuting family of Q-operators. The commutativity is equivalent to an elliptic hypergeometric integral transformation that was conjectured by Gadde et al., and has an alternative interpretation in terms of S-duality for quiver gauge theories. We present two proofs of this conjecture, one using the elliptic Macdonald polynomials of Langmann et al., and one using known results on elliptic hypergeometric integrals. We also explain how the Noumi-Sano operators appear as degenerations of Q-operators.
Cite
@article{arxiv.2503.18057,
title = {Q-operators for the Ruijsenaars model},
author = {Eric Rains and Hjalmar Rosengren},
journal= {arXiv preprint arXiv:2503.18057},
year = {2025}
}