Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems
Representation Theory
2023-02-20 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We present a shuffle realization of the GKLO-type homomorphisms for shifted quantum affine, toroidal, and quiver algebras, thus generalizing its rational version of arXiv:2104.14518 and the type A construction of arXiv:1811.12137. As an application, this allows us to construct large families of commuting and q-commuting difference operators, in particular, providing a convenient approach to the Q-systems where it proves a conjecture of arXiv:1704.00154.
Cite
@article{arxiv.2207.02804,
title = {Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems},
author = {Alexander Tsymbaliuk},
journal= {arXiv preprint arXiv:2207.02804},
year = {2023}
}
Comments
v2: 33 pages, few typos fixed, some details added. v1: 32 pages, comments are welcome!