Parametrizations of Unramified Tori

Abstract: If G is a reductive group over a p-adic field k, then DeBacker gives a paramaterization of the G(k)-conjugacy classes of maximal unramified k-tori using Bruhat–Tits theory. On the other hand, for classical groups, Waldspurger gives a parameterization in terms of triples of partitions. Given one of these triples, Waldspurger constructs a regular semisimple element for the maximal unramified torus by defining an endomorphism on an algebra whose structure is determined by the parts of the three partitions. After giving an overview of the two parameterizations, we will give a comparison, emphasizing the case of the symplectic group.

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