Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916263352074240 |
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| author | Ikeda, Takeshi Kouno, Takafumi Nakayama, Yusuke Yamaguchi, Kohei |
| author_facet | Ikeda, Takeshi Kouno, Takafumi Nakayama, Yusuke Yamaguchi, Kohei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism Ikeda, Takeshi Kouno, Takafumi Nakayama, Yusuke Yamaguchi, Kohei Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary 14M15, Secondary 53D45 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. |
| title | Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism |
| topic | Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary 14M15, Secondary 53D45 |
| url | https://arxiv.org/abs/2405.17854 |