Professor Alexander Stasinski alexander.stasinski@durham.ac.uk
Professor
The regular representations of GLN over finite local principal ideal rings
Stasinski, A.; Stevens, S.
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 |
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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
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