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Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems (2207.02804v2)
Published 6 Jul 2022 in math.RT, math-ph, math.MP, and math.QA
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.