English

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.

Keywords

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!

R2 v1 2026-06-24T12:16:12.885Z