Number theory seminar
Speaker: Manish Mishra (IISER Pune)
Title: Types and Hecke Algebras
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, December 6
Venue: Ramanujan Hall

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, jointly 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.