Two dimensional integral representations via branches of the Bruhat-Tits tree

2025/06/06 by Aguiló-Vidal, Bruno, Arenas-Carmona, Luis, Saavedra-Lagos, Matías · 1 citation
#11R56 (Secondary) #20C10 (Primary) 11R33 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.05661

Abstract

We apply the theory of branches in Bruhat-Tits trees, developed in previous works by the second author and others, to the study of two dimensional representations of finite groups over the ring of integers of a number field. We provide a general strategy to perform these computations, and we give explicit formulas for some particular families.

Citations

• Diophantine Approximation in local function fields via Bruhat-Tit trees
• On optimal embeddings and trees
• On some branches of the Bruhat-Tits tree
• Eichler orders, trees and Representation Fields

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• Computing quaternionic representations via twisted forms of Bruhat-Tits trees

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