6 papers
On some representations of Metacyclic groups whose integral forms can be computed from a single residual representation
Bruno Aguiló-Vidal, Luis Arenas-Carmona, Matías Saavedra-Lagos
In a previous work we computed the number of integral forms, over its field of definition, of an irreducible representation of a dihedral group. Here we apply the theory of Bruhat-…
Computing quaternionic representations via twisted forms of Bruhat-Tits trees
Luis Arenas-Carmona, Claudio Bravo
This work is devoted to the study of representations of finite subgroups of the group of units of quaternion division algebras over a global or local field arising from the inclusi…
Two dimensional integral representations via branches of the Bruhat-Tits tree
Bruno Aguiló-Vidal, Luis Arenas-Carmona, MatÃas Saavedra-Lagos
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…
Two characterizations of Bass orders via branches
Luis Arenas-Carmona
It has been known for some time that the orders in the four dimensional matrix algebra over a local field that can be written as a finite intersection of maximal orders are precise…
Eichler orders, quotient graphs and random walks
Luis Arenas-Carmona, Marco Godoy
We study the extent to which the quotient of the Bruhat-Tits tree at one place , associated to a genus of orders of maximal rank, can be computed from the analogous quotient at…
A Continued Fractions Theory for the completion of the Puiseux field
Luis Arenas-Carmona, Claudio Bravo
In this work, we study a continued fractions theory for the topological completion of the field of Puiseux series. As usual, we prove that any element in the completion can be deve…