École polytechnique  – Centre de Mathématiques Laurent Schwartz

14h00-14h45 : David Renard (CMLS)

"Exposé introductif : Représentations des groupes réductifs p-adiques et algèbres de Hecke "

14h55-15h50 : Chuan Qin (CMLS)

"On the involution of an affine Hecke algebra "

Summary: The study of duality on the representations over complex coefficients for finite Weyl groups and finite groups of Lie type can be traced back to the works of D. Alvis, C.W. Curtis, and L. Solomon in the 1970s. In this report, we will provide two generalizations of the Curtis-Alvis duality for Hecke algebras: the relative version for finite Hecke algebra based on Howlett-Lehrer's work and an unequal parameter version for affine Hecke algebras based on S-I.Kato's article. If time permits, we will also look at examples associated with the calculations for the principal series of the exceptional group G_2.