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K-theory of Gieseker variety and type A cyclotomic Hecke algebra

  • Vasily Krylov
  • Raphaël Paegelow
  • Pavel Shlykov
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{krylov2026ktheory,
  title = {{K-theory of Gieseker variety and type A cyclotomic Hecke algebra}},
  author = {Vasily Krylov and Raphaël Paegelow and Pavel Shlykov},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.11579},
  eprint = {2605.11579},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.11579},
}
RIS
TY  - UNPB
TI  - K-theory of Gieseker variety and type A cyclotomic Hecke algebra
AU  - Vasily Krylov
AU  - Raphaël Paegelow
AU  - Pavel Shlykov
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2605.11579
UR  - https://arxiv.org/abs/2605.11579
AB  - 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.
ER  -