A note on the structure theory of groups acting on the Bruhat Tits tree associated to PGL₂(F)

2013/04/28 by Inder Kaur, Kaur, Inder
Computer Science · Mathematics · #20E42 #20G25 #22E50 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1304.7490

openalex publication_date 2013/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove the classical decomposition theorems for certain subgroups of the automorphism group of the Bruhat-Tits tree associated to PGL₂(F), where F is a local field. The results can be used to understand the representation theory of these subgroups. Moreover, we can also use the results to obtain similar decompositions for any closed transitive subgroup of the automorphism group of any Bruhat-Tits tree.

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