Centralizers in Hecke Algebras of Any Coxeter Group

by Haiyu Chen (Chinese University of Hong Kong)

Monday 17 Nov 2025, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

We study the centralizer of a parabolic subalgebra in the Hecke algebra associated with an arbitrary (possibly infinite) Coxeter group. While the center and cocenter have been extensively studied in the finite and affine cases, much less is known in the indefinite setting. We describe a basis for the centralizer, generalizing known results about the center. Our approach combines algebraic techniques with geometric tools from the Davis complex, a CAT(0) space associated with the Coxeter group. As part of the construction, we classify finite partial conjugacy classes in infinite Coxeter groups and define a variant of the class polynomial adapted to the centralizer.