2022/09/17 by DeBacker, Stephen
#FOS: Mathematics #Group Theory (math.GR) #Primary 20G25 #Representation Theory (math.RT) #Secondary 22E35
paper · doi:10.48550/arxiv.2209.08389
Suppose k is a nonarchimedean local field, K is a maximally unramified extension of k, and G is a connected reductive k-group. In this paper we provide parameterizations via Bruhat-Tits theory of: the rational conjugacy classes of k-tori in G that split over K; the rational and stable conjugacy classes of the K-split components of the centers of unramified twisted Levi subgroups of G; and the rational conjugacy classes of unramified twisted generalized Levi subgroups of G. We also provide parameterizations of analogous objects for finite groups of Lie type.