Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems

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.

arXiv commentv2: 33 pages, few typos fixed, some details added. v1: 32 pages, comments are welcome!

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Cited by in corpus (1)

• Wreath Macdonald operators