Number Theory Seminar

Suppose G is an algebraic group defined over a nonarchimedian local field k. The G(k)-conjugacy classes of maximal k-tori in G play an important role in representation theory and harmonic analysis. One can understand these conjugacy classes via Galois cohomology, but this description doesn't provide much intuition for what the tori look like, how they embed into G, or how they interact with parahoric subgroups of G. In this talk we will discuss a parameterization of the G(k)-conjugacy classes of maximal k-tori in G via Bruhat-Tits theory.