Coefficients of the local character expansion are motivic

Abstract: In 1994, M. Assem observed that with a suitable choice of Haar measures, the unipotent orbital integrals on a connected reductive group G over a p-adic field are rational-valued for rational-valued test functions. He concluded that Shalika germs, and in some cases, the coefficients of the Harish-Chandras local character expansion are rational, and conjectured that it should always be the case. I will try to outline a proof of the general case, which now uses the new kind of local character expansion due to Loren Spice, and motivic integration (to get a uniform result for almost all local fields). This is joint work in progress with Thomas Hales and Loren Spice.

number theoryrepresentation theory

Audience: researchers in the discipline

The 2020 Paul J. Sally, Jr. Midwest Representation Theory Conference

Series comments: The 44th Midwest Representation Theory Conference will address recent progress in the theory of representations for groups over non-archimedean local fields, and connections of this theory to other areas within mathematics, notably number theory and geometry.

In order to receive information on how to participate (to be sent out closer to the conference), please register by October 14 here: forms.gle/zFAnQBnuPGRnKzMr7