An Elliptic Generalization of $A_1$ Spherical DAHA at $K=2$
Quantum Algebra
2023-06-06 v1 Mathematical Physics
math.MP
Rings and Algebras
Representation Theory
Abstract
We construct an algebra that is an elliptic generalization of spherical DAHA acting on its finite-dimensional module at with . We prove that acts by automorphisms of the algebra we constructed, and provide an explicit representation of automorphisms and algebra operators alike by matrices of elliptic functions. A relation of this construction to the K-theory character of affine Laumon space is conjectured. We point out two potential applications, respectively to symmetry of Felder-Varchenko functions and to new elliptic invariants of torus knots and Seifert manifolds.
Keywords
Cite
@article{arxiv.2306.00215,
title = {An Elliptic Generalization of $A_1$ Spherical DAHA at $K=2$},
author = {S. Arthamonov and Sh. Shakirov},
journal= {arXiv preprint arXiv:2306.00215},
year = {2023}
}
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32 pages