Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms

Abstract: The category of smooth complex representations of $p$-adic groups decomposes into a product of indecomposable full subcategories, called Bernstein blocks. In this talk, I will explain the result that under a mild tameness condition, every block is equivalent to a depth-zero block, which is closely related to the representation theory of finite reductive groups and much better understood than general blocks. This result is obtained by using the theory of types and an isomorphism of Hecke algebras. This is a joint work with Jeffrey Adler, Jessica Fintzen, and Manish Mishra.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html