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arXiv · 2405.17854

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

Takeshi Ikeda·Takafumi Kouno·Yusuke Nakayama·Kohei Yamaguchi
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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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Takeshi Ikeda, Takafumi Kouno, Yusuke Nakayama, Kohei Yamaguchi. 2024-05-28. Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism. https://arxiv.org/abs/2405.17854

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