Regular characters of groups of type An over discrete valuation rings

Roi Krakovski, Uri Onn*, Pooja Singla

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    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 ℓ, let K be the ℓ-th principal congruence subgroup of G(o). A continuous irreducible representation of G(o) is called regular of level ℓ if it is trivial on Kℓ+1 and its restriction to K/Kℓ+1≃g(k) consists of characters with G(k‾)-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.

    Original languageEnglish
    Pages (from-to)116-137
    Number of pages22
    JournalJournal of Algebra
    Volume496
    DOIs
    Publication statusPublished - 15 Feb 2018

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