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 |
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Full text: | (AM) Accepted Manuscript Download PDF (391Kb) |
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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