$p$-adic representations of $p$-adic groups

Working Seminar on Representation Theory
Topic:$p$-adic representations of $p$-adic groups
Speaker:Daniel Le
Affiliation:Member, School of Mathematics
Date:Wednesday, November 16
Time/Room:11:00am - 12:00pm/S-101

In the 80's, Bernstein calculated the center of the category of smooth admissible characteristic zero representations of $p$-adic reductive groups and related it to the Bernstein--Zelevinsky classification. In 2010, Paskunas set up a similar theory of the center with $p$-torsion coefficients and computed the center in the case of $\mathrm{GL}_2(\mathbb Q_p)$ using the $p$-adic local Langlands correspondence of Colmez. As a corollary, he obtained a classification (prima facie very different from Bernstein--Zelevinsky) of integral and Banach space representations of $\mathrm{GL}_2(\mathbb Q_p)$. We will describe some elements of Paskunas's work.