Time: 10:00-11:00, Thursday, January 22 2026
Venue: E14-212
Speaker: Chuan Qin
Titile: Involution for the representations of Hecke algebras
Abstract: In this report, we present two generalizations of the Alvis-Curtis-Kawanaka (ACK) duality for Hecke algebras: a relative version for finite Hecke algebras, based on Howlett-Lehrer's work (under certain assumptions), and an unequal parameter version for affine Hecke algebras, based on the work of S.-I. Kato. By requiring the involution to be compatible with ACK duality/Aubert-Zelevinsky duality on the group side and restricting to a fixed Harish-Chandra series/Bernstein block, we obtain the "left-hand side" of the involution for modules of finite and affine Hecke algebras. Additionally, we provide an interpretation of the generalization of Howlett-Lehrer's work for finite Hecke algebras under these conditions. If time permits, we will also look at some examples.
