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.
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.
|Full text:||(AM) Accepted Manuscript|
Download PDF (391Kb)
|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|
Save or Share this output
|Look up in GoogleScholar|