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Seminars

Seminar in Representation Theory

Affine and asymptotic Hecke algebras and p-adic groups

2025/01/15 (Wed.) 15:30~16:30
  • Date : 2025/01/15 (Wed.) 15:30~16:30
  • Location : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
  • Speaker : Stefan Dawydiak (University of Bonn)
  • Organizer : Cheng-Chiang Tsai (AS)
  • Abstract : The role of affine Hecke algebras in the representation theory of p-adic groups has recently grown to account for the entire theory. On the other hand, it is expected that an enlargement of the class of standard representations of a p-adic group should admit an interpretation in terms of the geometrization of the local Langlands correspondence by Fargues-Scholze. I will provide some evidence for a description of this conjectural class in terms of (asymptotic) affine Hecke algebras, building on work of Braverman-Kazhdan, and earlier work of Lusztig. I will also survey some geometric incarnations of asymptotic Hecke algebras in the case of equal parameters, and some resulting applications.
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