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

• Author(s): Dias, João Miguel Cardoso
• Date: 2020
• Persistent ID: http://hdl.handle.net/10451/45594
• Origin: Repositório da Universidade de Lisboa
• Project/scholarship: info:eu-repo/grantAgreement/FCT/OE/PD%2FBD%2F52641%2F2014/PT
• Subject(s): Algebra group; unit group; smooth representation; induction with compact supports; Gutkin’s conjecture; Domínio/Área Científica::Ciências Naturais::Matemáticas
• Document Type: Doctoral thesis
• Language: English
• Advisor(s): André, Carlos Alberto Martins
• Contributor(s): Repositório da Universidade de Lisboa

Description

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.