View in EDS

On representations of GL2 over finite chain rings.

Saved in:
Bibliographic Details
Title: On representations of GL2 over finite chain rings.
Authors: Dagar, Prem1 (AUTHOR) prem_d@ma.iitr.ac.in, Verma, Mahendra Kumar1 (AUTHOR) mahendraverma@ma.iitr.ac.in
Source: Linear Algebra & its Applications. Apr2026, Vol. 734, p73-88. 16p.
Subjects: Local fields (Algebra), Representation theory, Finite rings, Whittaker functions
Abstract: Let F be a non-Archimedean local field and O be its ring of integers with ϖ chosen as a fixed generator for the maximal ideal of O. Define O ℓ : = O / 〈 ϖ ℓ 〉 as the finite local ring. In this paper, we describe the explicit construction of parabolically induced representations of the group GL 2 (O ℓ) for ℓ > 1 and establish an irreducibility criterion for these representations. Additionally, we determine the number of irreducible constituents in the case of reducibility. Furthermore, we study the primitive cuspidal representations and explore the representations of GL 2 (O ℓ) using the Whittaker and Kirillov model. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 191077541
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On representations of GL2 over finite chain rings.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Dagar%2C+Prem%22">Dagar, Prem</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> prem_d@ma.iitr.ac.in</i><br /><searchLink fieldCode="AR" term="%22Verma%2C+Mahendra+Kumar%22">Verma, Mahendra Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mahendraverma@ma.iitr.ac.in</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Apr2026, Vol. 734, p73-88. 16p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Local+fields+%28Algebra%29%22">Local fields (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+rings%22">Finite rings</searchLink><br /><searchLink fieldCode="DE" term="%22Whittaker+functions%22">Whittaker functions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Let F be a non-Archimedean local field and O be its ring of integers with ϖ chosen as a fixed generator for the maximal ideal of O. Define O ℓ : = O / 〈 ϖ ℓ 〉 as the finite local ring. In this paper, we describe the explicit construction of parabolically induced representations of the group GL 2 (O ℓ) for ℓ > 1 and establish an irreducibility criterion for these representations. Additionally, we determine the number of irreducible constituents in the case of reducibility. Furthermore, we study the primitive cuspidal representations and explore the representations of GL 2 (O ℓ) using the Whittaker and Kirillov model. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=191077541
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.laa.2025.12.023
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 73
    Subjects:
      – SubjectFull: Local fields (Algebra)
        Type: general
      – SubjectFull: Representation theory
        Type: general
      – SubjectFull: Finite rings
        Type: general
      – SubjectFull: Whittaker functions
        Type: general
    Titles:
      – TitleFull: On representations of GL2 over finite chain rings.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Dagar, Prem
      – PersonEntity:
          Name:
            NameFull: Verma, Mahendra Kumar
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 00243795
          Numbering:
            – Type: volume
              Value: 734
          Titles:
            – TitleFull: Linear Algebra & its Applications
              Type: main
ResultId 1