Smooth representations of Groups associated with Algebras defined over non-archimedean fields

Abstract

In this thesis, we study smooth representations of algebra groups, involutive algebra groups and unit groups of split basic algebras. We prove that every smooth irreducible representation of such a group is induced by a smooth representation of dimension one, which correspond to a continuous character of a subgroup of the same type. We also prove results about admissibility and unitarisability. This work generalises work of C. André and Z. Halasi who proved similar results in the case of finite fields, and is based on a method introduced by M. Boyarchenko for the case of algebra groups over local non-Archimedean fields.