A Gelfand-Graev Formula and Stable Transfer Factors for $\mathrm{SL}_n$

Working Seminar on Representation Theory
Topic:A Gelfand-Graev Formula and Stable Transfer Factors for $\mathrm{SL}_n$
Speaker:Daniel Johnstone
Affiliation:University of Chicago
Date:Friday, January 27
Time/Room:2:00pm - 3:00pm/S-101

A result of Gelfand and Graev shows that the supercuspidal representations of $\mathrm{SL}_2$ are neatly parameterized by characters of elliptic tori, and that the stable character data for all such representations may be collected into a single function by means of a Fourier Transform. Using recent advances in the computation of characters of supercuspidal representations, we prove analogous results for the group $\mathrm{SL}_n$.