Skip to main content

Research Repository

Advanced Search

The regular representations of GLN over finite local principal ideal rings

Stasinski, A.; Stevens, S.

The regular representations of GLN over finite local principal ideal rings Thumbnail


Authors

S. Stevens



Abstract

Let o o be the ring of integers in a non-Archimedean local field with finite residue field, p p its maximal ideal, and r ⩾ 2 r⩾2 an integer. An irreducible representation of the finite group G r = GL N ( o / p r ) Gr=GLN(o/pr), for an integer N ⩾ 2 N⩾2, is called regular if its restriction to the principal congruence kernel K r − 1 = 1 + p r − 1 M N ( o / p r ) Kr−1=1+pr−1MN(o/pr) consists of representations whose stabilisers modulo K 1 K1 are centralisers of regular elements in M N ( o / p ) MN(o/p). The regular representations form the largest class of representations of G r Gr which is currently amenable to explicit construction. Their study, motivated by constructions of supercuspidal representations, goes back to Shintani, but the general case remained open for a long time. In this paper we give an explicit construction of all the regular representations of G r Gr.

Citation

Stasinski, A., & Stevens, S. (2017). The regular representations of GLN over finite local principal ideal rings. Bulletin of the London Mathematical Society, 49(6), 1066-1084. https://doi.org/10.1112/blms.12099

Journal Article Type Article
Acceptance Date Aug 30, 2017
Online Publication Date Oct 19, 2017
Publication Date Oct 19, 2017
Deposit Date Sep 26, 2017
Publicly Available Date Mar 29, 2024
Journal Bulletin of the London Mathematical Society
Print ISSN 0024-6093
Electronic ISSN 1469-2120
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 49
Issue 6
Pages 1066-1084
DOI https://doi.org/10.1112/blms.12099
Related Public URLs https://arxiv.org/abs/1611.04796

Files

Accepted Journal Article (400 Kb)
PDF

Copyright Statement
This is the accepted version of the following article: Stasinski, A. & Stevens, S. (2017). The regular representations of GLN over finite local principal ideal rings. Bulletin of the London Mathematical Society 49(6): 1066-1084. The regular representations of GLN over finite local principal ideal rings. Bulletin of the London Mathematical Society, which has been published in final form at https://doi.org/10.1112/blms.12099




You might also like



Downloadable Citations