Genus Two Generalization of $A_1$ spherical DAHA
Quantum Algebra
2019-09-20 v1 High Energy Physics - Theory
Representation Theory
Abstract
We consider a system of three commuting difference operators in three variables with two generic complex parameters . This system and its eigenfunctions generalize the trigonometric Ruijsenaars-Schneider model and Macdonald polynomials, respectively. The principal object of study in this paper is the algebra generated by these difference operators together with operators of multiplication by . We represent the Dehn twists by outer automorphisms of this algebra and prove that these automorphisms satisfy all relations of the mapping class group of the closed genus two surface. Therefore we argue from topological perspective this algebra is a genus two generalization of spherical DAHA.
Cite
@article{arxiv.1704.02947,
title = {Genus Two Generalization of $A_1$ spherical DAHA},
author = {S. Arthamonov and Sh. Shakirov},
journal= {arXiv preprint arXiv:1704.02947},
year = {2019}
}