A remark on conductor, depth and principal congruence subgroups

TL;DR

This paper explores the relationships between conductor, depth, and principal congruence subgroup levels in irreducible admissible representations of GL_n over non-archimedean local fields, with some global and local applications.

Contribution

It establishes new connections between conductor, depth, and principal congruence subgroup levels for these representations, providing insights for further research.

Findings

Identifies relations between conductor and depth.

Analyzes the level of principal congruence subgroups.

Discusses applications in global and local contexts.

Abstract

In this paper we study a relation between conductor, depth, and the level of principal congruence subgroups for irreducible admissible representations of ${\rm GL}_n(F)$ for a non-archimedean local field $F$ of characteristic zero. Some global and local applications are also discussed.