Orateur : Chuan Qin
Établissement : IMJ-PRG ()
Dates : 2024-10-10 – 2024-10-10
Heures : 14:00 – 14:00
Lieu : Salle 0-6
Résumé :
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