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Quantum Integrability and Generalised Quantum Schubert Calculus

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arxiv 1408.4718 v4 pith:YCANKWYN submitted 2014-08-20 math.RT math.AGmath.KTmath.QAnlin.SI

Vassily Gorbounov , Christian Korff This is my paper · ORCID
classification math.RTmath.AGmath.KTmath.QAnlin.SI
keywords quantumcalculusequivariantgeneralisedk-theoryschubertadditionallows
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We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.

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Cited by 2 Pith papers

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

  1. Schubert defects in Lagrangian Grassmannians

    hep-th 2025-02 conditional novelty 6.0 of 10

    A GLSM defect construction for Schubert cycles in Lagrangian Grassmannians is proposed and checked, with defect indices equal to Schur Q-functions in quantum cohomology and quantum K theory.

  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.

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