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Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism

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arxiv 2405.17854 v1 pith:QJ6JEYDF submitted 2024-05-28 math.AG math.COmath.KTmath.RT

Takeshi Ikeda , Takafumi Kouno , Yusuke Nakayama , Kohei Yamaguchi This is my paper · ORCID
classification math.AGmath.COmath.KTmath.RT
keywords mathrmgrassmannianquantumringlagrangianlocalizedpetersontorus-equivariant
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abstract

We study Schubert calculus in the torus-equivariant quantum $K$-ring of the Lagrangian Grassmannian $\mathrm{LG}(n)$. Our main tool is the $K$-theoretic Peterson map due to Kato. The map is from the (localized) equivariant $K$-homology ring $K_{*}^{T}(\mathrm{Gr}_{G})$ of the affine Grassmannian $\mathrm{Gr}_{G}$ of the symplectic group $G=\mathrm{Sp}_{2n}(\mathbb{C})$ to the (localized) torus-equivariant quantum $K$-ring $QK_{T}(\mathrm{LG}(n))$. We determine explicitly the kernel of this map.

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  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.

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