Mathematics Seminar
Date: Friday, 15 March 2024
Time: 11.50 AM to 12:50 PMs
Venue: Seminar Hall
Types and Hecke algebras
Manish Mishra
IISER Pune.
15-03-24

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Abstract

Let R(G) denote the category of smooth complex representation of G(F), where G is a connected reductive group defined over a non-archimedean local field F. Bernstein decomposition expresses R(G) as a product of indecomposable subcategories called Bernstein blocks. Each Bernstein block is equivalent to the module category of the "Hecke algebra" associated with that "type". I will go over the basic theory mentioned above. To each Bernstein block, the theory of Moy and Prasad associates a number called depth. I will describe a result, part of a work in progress jointly being done with Jeff Adler, Jessica Fintzen and Kazuma Ohara, which states that each Bernstein block is equivalent to a depth-zero Bernstein block of a certain subgroup of G, when the residue characteristic is not too small.