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Multiplicative slices, relativistic Toda and shifted quantum affine algebras

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arxiv 1708.01795 v6 pith:N7ZDXIG7 submitted 2017-08-05 math.RT math-phmath.AGmath.MPmath.QA

Michael Finkelberg , Alexander Tsymbaliuk This is my paper · ORCID
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keywords theyquantumtypeaffinealgebrasrelativisticshiftedtoda
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abstract

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.

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Cited by 1 Pith paper

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  1. Jordan-H\"older property for shifted quantum affine algebras

    math.QA 2025-01 conditional novelty 7.0 of 10

    Finite-length representations of shifted quantum affine algebras are stable under fusion product, yielding an ordinary subring and a new route to cluster algebra isomorphisms.

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