Loop structure on equivariant $K$-theory of semi-infinite flag manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866929646878064640 |
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| author | Kato, Syu |
| author_facet | Kato, Syu |
| contents | We explain that the Pontryagin product structure on the equivariant $K$-group of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math. {\bf 146} (2010)] coincides with the tensor structure on the equivariant $K$-group of a semi-infinite flag manifold considered in [K-Naito-Sagaki, Duke Math. {\bf 169} (2020)]. Then, we construct an explicit isomorphism between the equivariant $K$-group of a semi-infinite flag manifold with a suitably localized equivariant quantum $K$-group of the corresponding flag manifold. These exhibit a new framework to understand the ring structure of equivariant quantum $K$-theory and the Peterson isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_01718 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Loop structure on equivariant $K$-theory of semi-infinite flag manifolds Kato, Syu Algebraic Geometry Quantum Algebra Representation Theory We explain that the Pontryagin product structure on the equivariant $K$-group of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math. {\bf 146} (2010)] coincides with the tensor structure on the equivariant $K$-group of a semi-infinite flag manifold considered in [K-Naito-Sagaki, Duke Math. {\bf 169} (2020)]. Then, we construct an explicit isomorphism between the equivariant $K$-group of a semi-infinite flag manifold with a suitably localized equivariant quantum $K$-group of the corresponding flag manifold. These exhibit a new framework to understand the ring structure of equivariant quantum $K$-theory and the Peterson isomorphism. |
| title | Loop structure on equivariant $K$-theory of semi-infinite flag manifolds |
| topic | Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/1805.01718 |