GAMP-seminar by Alex Kemarsky

Alex Kemarsky: A new bound for Bernstein's uniform admissibility theorem

Abstract: In "All p-adic reductive groups are tame" Bernstein proved that for a reductive group G over a local non-archimedean field F and a compact open subgroup K of G there exists a uniform bound C(G,K) such that every irreducible, smooth, and admissible representation V of G satisfies dim(V^K) < C(G,K).  In the talk I will repeat the proof of Bernstein and give my proof to one of the two main lemmas. The new proof of this lemma will give a new, sharper bound for the constant C(G,K).