Principal series for general linear groups over finite commutative rings

Tyrone Crisp; Ehud Meir Ben Efraim; Uri Onn

doi:10.1080/00927872.2021.1931264

Principal series for general linear groups over finite commutative rings

Tyrone Crisp, Ehud Meir Ben Efraim^* (Corresponding Author), Uri Onn

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

3 Downloads (Pure)

Abstract

We construct, for any finite commutative ring R, a family of representations of the general linear group GLnðRÞ whose intertwining properties mirror those of the principal series for GLn over a finite field.

Original language	English
Pages (from-to)	4857-4868
Number of pages	12
Journal	Communications in Algebra
Volume	49
Issue number	11
Early online date	5 Jun 2021
DOIs	https://doi.org/10.1080/00927872.2021.1931264
Publication status	Published - 2021

Bibliographical note

Open access via T&F agreement
Fundings: Australian Research Council / Danmarks Grundforskningsfond / German Research Foundation / Israel Science Foundation / Max-Planck-Gesellschaft / Radboud Universiteit
Funding
The first and second authors were partly supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The first author was also supported by fellowships from the Max Planck Institute for Mathematics in Bonn, and from the Radboud Excellence Initiative at Radboud University Nijmegen. The second author was also supported by the Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory.” The third author acknowledges the support of the Israel Science Foundation [grant number 1862/16] and of the Australian Research Council [grant number FT160100018].

Keywords

Finite commutative rings
general linear groups
principal series

Access to Document

10.1080/00927872.2021.1931264Licence: CC BY-NC-ND

Crisp_etal_CA_Principal_Series_For_VoR
© 2021 The Author(s). Published with license by Taylor and Francis Group, LLC This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Final published version, 1.45 MBLicence: CC BY-NC-ND

Cite this

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title = "Principal series for general linear groups over finite commutative rings",

abstract = "We construct, for any finite commutative ring R, a family of representations of the general linear group GLn{\dh}R{\TH} whose intertwining properties mirror those of the principal series for GLn over a finite field.",

keywords = "Finite commutative rings, general linear groups, principal series",

author = "Tyrone Crisp and {Meir Ben Efraim}, Ehud and Uri Onn",

note = "Open access via T&F agreement Fundings: Australian Research Council / Danmarks Grundforskningsfond / German Research Foundation / Israel Science Foundation / Max-Planck-Gesellschaft / Radboud Universiteit Funding The first and second authors were partly supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The first author was also supported by fellowships from the Max Planck Institute for Mathematics in Bonn, and from the Radboud Excellence Initiative at Radboud University Nijmegen. The second author was also supported by the Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory.” The third author acknowledges the support of the Israel Science Foundation [grant number 1862/16] and of the Australian Research Council [grant number FT160100018]. ",

year = "2021",

doi = "10.1080/00927872.2021.1931264",

language = "English",

volume = "49",

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journal = "Communications in Algebra",

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T1 - Principal series for general linear groups over finite commutative rings

AU - Crisp, Tyrone

AU - Meir Ben Efraim, Ehud

AU - Onn, Uri

N1 - Open access via T&F agreement Fundings: Australian Research Council / Danmarks Grundforskningsfond / German Research Foundation / Israel Science Foundation / Max-Planck-Gesellschaft / Radboud Universiteit Funding The first and second authors were partly supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The first author was also supported by fellowships from the Max Planck Institute for Mathematics in Bonn, and from the Radboud Excellence Initiative at Radboud University Nijmegen. The second author was also supported by the Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory.” The third author acknowledges the support of the Israel Science Foundation [grant number 1862/16] and of the Australian Research Council [grant number FT160100018].

PY - 2021

Y1 - 2021

N2 - We construct, for any finite commutative ring R, a family of representations of the general linear group GLnðRÞ whose intertwining properties mirror those of the principal series for GLn over a finite field.

AB - We construct, for any finite commutative ring R, a family of representations of the general linear group GLnðRÞ whose intertwining properties mirror those of the principal series for GLn over a finite field.

KW - Finite commutative rings

KW - general linear groups

KW - principal series

U2 - 10.1080/00927872.2021.1931264

DO - 10.1080/00927872.2021.1931264

M3 - Article

SN - 0092-7872

VL - 49

SP - 4857

EP - 4868

JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

Principal series for general linear groups over finite commutative rings

Abstract

Bibliographical note

Keywords

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