Regular characters of groups of type An over discrete valuation rings

Roi Krakovski, Uri Onn, Pooja Singla

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
StatePublished - 15 Feb 2018
Externally publishedYes


  • Ennola duality
  • Representation zeta functions
  • Representations of compact p-adic groups

ASJC Scopus subject areas

  • Algebra and Number Theory


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