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

TL;DR

This paper introduces a new approach using Bruhat-Tits trees to analyze two-dimensional representations of finite groups over number field rings, providing explicit formulas and a general computational strategy.

Contribution

It develops a novel method leveraging Bruhat-Tits trees for studying such representations, with explicit formulas and a systematic approach.

Findings

Explicit formulas for specific families of representations

A general strategy for computations in this context

Enhanced understanding of the structure of 2D representations

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.