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

Stasinski, A. and Stevens, S. (2017) 'The regular representations of GLN over finite local principal ideal rings.', Bulletin of the London Mathematical Society., 49 (6). pp. 1066-1084.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1112/blms.12099
Publisher 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
Date accepted:30 August 2017
Date deposited:27 September 2017
Date of first online publication:19 October 2017
Date first made open access:No date available

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