Speaker: 胡峻教授，北京理工大学

Inviter: 方明

Title: On the center conjectures for the cyclotomic Hecke and KLR algebras

Language: English

Time & Venue: 2026.11.05 10:30-11:25 南楼N820

Abstract: I shall report my recent joint work (arXiv:2610.25101) with Andrew Mathas, Lei Shi and Ben Webster on the proof of the center conjecture for the cyclotomic Hecke algebra. We show that, for any quiver without edge loops, there is an isomorphism from the cohomology of a Nakajima quiver variety with coefficients in an arbitrary field to the Jucys–Murphy center of the corresponding cyclotomic KLR algebra. In affine type A, combining this with a dimension count by the author and Shi, this implies Jucys–Murphy center coincides with the full center in characteristic 0, when the characteristic does not divide e, and when the characteristic equals e. As applications, we deduce the center conjectures for the cyclotomic Hecke algebra. We also verify the conjecture of Krylov, Paegelow and Shlykov identifying the equivariant K-theory of the core of a Gieseker variety with the cocenter of the generic cyclotomic Hecke algebra.