Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896486 | Journal of Algebra | 2018 | 22 Pages |
Abstract
Let o be a complete discrete valuation ring with finite residue field k of odd characteristic. Let G be a general or special linear group or a unitary group defined over o and let g denote its Lie algebra. For every positive integer â, let Kâ be the â-th principal congruence subgroup of G(o). A continuous irreducible representation of G(o) is called regular of level â if it is trivial on Kâ+1 and its restriction to Kâ/Kâ+1âg(k) consists of characters with G(kâ¾)-stabiliser of minimal dimension. In this paper we construct the regular characters of G(o), compute their degrees and show that the latter satisfy Ennola duality. We give explicit uniform formulae for the regular part of the representation zeta functions of these groups.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Roi Krakovski, Uri Onn, Pooja Singla,