2023/09/16 by Stephen DeBacker, DeBacker, Stephen · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Primary 20G25 #Representation Theory (math.RT) #Secondary 22E35 #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2309.09049
openalex publication_date 2023/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose k is a nonarchimedean local field, K is a maximally unramified extension of k, and G is a connected reductive k-group. If T is a K-minisotropic maximal k-torus in G, then we use Bruhat-Tits theory to describe the stable classes in the G-orbit of T, the rational classes in the G-orbit of T, and the k-embeddings, up to rational conjugacy, into G of T. We also provide, via Bruhat-Tits theory, a complete and explicit description of: the rational conjugacy classes of K-minisotropic maximal tame k-tori in G; the stable classes of K-minisotropic maximal tame k-tori in G; and the k-embeddings, up to rational conjugacy, into G of a K-minisotropic maximal tame k-torus of G.