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

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arxiv 2207.02804 v2 pith:A2G6ZXWJ submitted 2022-07-06 math.RT math-phmath.MPmath.QA

Alexander Tsymbaliuk This is my paper · ORCID
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keywords arxivapplicationapproachdifferencegklo-typehomomorphismsoperatorsq-systems
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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.

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  1. Quantum Trigonometric Spin Ruijsenaars-Schneider Models from $K$-theoretic Coulomb Branches

    hep-th 2026-07 conditional novelty 8.0 of 10

    The trigonometric spin Ruijsenaars-Schneider model is quantized from K-theoretic Coulomb branch data, with commuting Hamiltonians and quantum spin commutation relations derived.

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