The Bernstein Center of the Category of Smooth W(k)[GL_n(F)]-Modules

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:The Bernstein Center of the Category of Smooth W(k)[GL_n(F)]-Modules
Speaker:David Helm
Affiliation:University of Texas
Date:Thursday, April 14
Time/Room:2:15pm - 3:15pm/S-101
Video Link:https://video.ias.edu/galois/helm

The Bernstein center plays a role in the representation theory of locally profinite groups analogous to that played by the center of the group ring in the representation theory of finite groups. When F is a finite extension of Q_p, we discuss the Bernstein center of the category of smooth representations of GL_n(F) over the Witt vectors of an algebraically closed field of characteristic l not equal to p. We will prove results on the basic structure of the Bernstein center, and describe a conjecture that has implications for the local Langlands correspondence in algebraic families.