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Quantum K-theory of Quiver Varieties and Many-Body Systems

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arxiv 1705.10419 v5 pith:MDKZ6QRE submitted 2017-05-30 math.AG hep-thmath-phmath.MPmath.RT

Peter Koroteev , Petr P. Pushkar , Andrey Smirnov , Anton M. Zeitlin This is my paper · ORCID
classification math.AGhep-thmath-phmath.MPmath.RT
keywords quantumvarietiesk-theoryquiverchainsconnectingconnectionsdefine
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We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum K-theory levels in physics and math

    hep-th 2025-06 conditional novelty 6.0 of 10

    Chern-Simons levels and Ruan-Zhang levels are identified as the same twisting of quantum K-theory, with Coulomb branch equations matching difference operator symbols and geometric windows matching mirror triviality.

  2. Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\beta$-Grothendieck polynomials

    math-ph 2025-02 conditional novelty 6.0 of 10

    Bethe ansatz states of a new GL(n) five vertex model expand into double β-Grothendieck polynomials, and the model's Bethe equations reproduce the quantum Whitney relations of flag varieties.

  3. On the Quantum K-theory of Quiver Varieties at Roots of Unity

    math.AG 2024-12 conditional novelty 6.0 of 10

    At q a primitive p-th root of unity, the iterated quantum shift operator on a Nakajima variety has the same spectrum as quantum multiplication with all Kähler and equivariant parameters raised to the p-th power.

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