K-theory of Gieseker variety and type A cyclotomic Hecke algebra
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| Format: | Preprint |
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2026
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| _version_ | 1866910252087115776 |
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| author | Krylov, Vasily Paegelow, Raphaël Shlykov, Pavel |
| author_facet | Krylov, Vasily Paegelow, Raphaël Shlykov, Pavel |
| contents | We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point. The construction is inspired by the proof of the Hikita--Nakajima conjecture for Gieseker spaces given by the first and third authors. We discuss consequences for the center of cyclotomic Hecke algebras and for specializations to q=1 and to roots of unity. In particular, we relate K-theory of affine type A quiver varieties with the centers of the corresponding blocks of specialized cyclotomic Hecke algebras. This last result strengthens the correspondences obtained by the second author in earlier work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11579 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | K-theory of Gieseker variety and type A cyclotomic Hecke algebra Krylov, Vasily Paegelow, Raphaël Shlykov, Pavel Algebraic Geometry Representation Theory We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point. The construction is inspired by the proof of the Hikita--Nakajima conjecture for Gieseker spaces given by the first and third authors. We discuss consequences for the center of cyclotomic Hecke algebras and for specializations to q=1 and to roots of unity. In particular, we relate K-theory of affine type A quiver varieties with the centers of the corresponding blocks of specialized cyclotomic Hecke algebras. This last result strengthens the correspondences obtained by the second author in earlier work. |
| title | K-theory of Gieseker variety and type A cyclotomic Hecke algebra |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2605.11579 |