A remark on conductor, depth and principal congruence subgroups

Michitaka Miyauchi; Takuya Yamauchi

doi:10.1016/j.jalgebra.2021.10.032

A remark on conductor, depth and principal congruence subgroups

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Abstract

In this paper we study a relation between conductor, depth, and the level of principal congruence subgroups for irreducible admissible representations of GL_n(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 GL_n(A_Q) 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.

Original language	English
Pages (from-to)	424-434
Number of pages	11
Journal	Journal of Algebra
Volume	592
DOIs	https://doi.org/10.1016/j.jalgebra.2021.10.032
Publication status	Published - Feb 15 2022

Keywords

Conductor
Depth
Principal congruence subgroups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2021.10.032

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title = "A remark on conductor, depth and principal congruence subgroups",

abstract = "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.",

keywords = "Conductor, Depth, Principal congruence subgroups",

author = "Michitaka Miyauchi and Takuya Yamauchi",

note = "Funding Information: The first author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778 . The second author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778 . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AU - Yamauchi, Takuya

N1 - Funding Information: The first author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778 . The second author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778 . Publisher Copyright: © 2021 Elsevier Inc.

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N2 - 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.

AB - 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.

KW - Conductor

KW - Depth

KW - Principal congruence subgroups

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DO - 10.1016/j.jalgebra.2021.10.032

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VL - 592

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EP - 434

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A remark on conductor, depth and principal congruence subgroups

Abstract

Keywords

ASJC Scopus subject areas

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