In this paper we study a relation between conductor, depth, and the level of principal congruence subgroups for irreducible admissible representations of GLn(F) for a non-archimedean local field F of characteristic zero. As a global application, we estimate conductors of unitary irreducible automorphic cuspidal representations of GLn(AQ) in terms of principal congruence subgroups. We also give an explicit formula for the dimension of fixed vectors with respect to principal congruence subgroups for irreducible admissible representations of GL2(F) as a local application.
- Principal congruence subgroups
ASJC Scopus subject areas
- Algebra and Number Theory