The regular representations of GLN over finite local principal ideal rings

Stasinski, Alexander and Stevens, Shaun (2017) The regular representations of GLN over finite local principal ideal rings. Bulletin of the London Mathematical Society, 49 (6). 1066–1084. ISSN 0024-6093

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Abstract

Let o be the ring of integers in a non-Archimedean local field with finite residue field, p its maximal ideal, and r ≥ 2 an integer. An irreducible representation of the finite group Gr = GLN (o/p r ), for an integer N ≥ 2, is called regular if its restriction to the principal congruence kernel Kr−1 = 1 + pr−1 MN (o/pr ) consists of representations whose stabilisers modulo K1 are centralisers of regular elements in MN (o/p).  The regular representations form the largest class of representations of 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 Gr.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	06 Sep 2017 05:06
Last Modified:	07 Nov 2024 12:39
URI:	https://ueaeprints.uea.ac.uk/id/eprint/64761
DOI:	10.1112/blms.12099

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