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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

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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  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.

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