Date(s) : 07/04/2017 iCal
14 h 00 min - 17 h 00 min
Affine Hecke algebras and their representations.
The aim of these lectures is to offer an overview of harmonic analysis for affine Hecke algebras and the relations with smooth representations of reductive p-adic groups. I will explain first how affine Hecke algebras appear naturally in the world of representations of p-adic groups as Iwahori-Hecke algebras, and as endomorphism algebras of certain projective generators.
I will show how certain important questions in harmonic analysis for p-adic groups can be translated to affine Hecke algebras: e.g., the Plancherel formula and the determination of the unitary dual. I will explain the classification and construction of discrete series modules for affine Hecke algebras with unequal parameters, the calculation of formal degrees, the density and trace Paley-Wiener theorems in this setting, and, if time permits, present some elements of the theory of Dirac operators for graded affine Hecke algebras.
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