Regular characters of classical groups over complete discrete valuation rings

Shai Shechter

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let o be a complete discrete valuation ring with finite residue field k of odd characteristic, and let G be a symplectic or special orthogonal group scheme over o. For any ℓ∈N let G denote the ℓ-th principal congruence subgroup of G(o). An irreducible character of the group G(o)is said to be regular if it is trivial on a subgroup G ℓ+1 for some ℓ, and if its restriction to G /G ℓ+1 ≃Lie(G)(k)consists of characters of minimal G(k alg )-stabilizer dimension. In the present paper we consider the regular characters of such classical groups over o, and construct and enumerate all regular characters of G(o), when the characteristic of k is greater than two. As a result, we compute the regular part of their representation zeta function.

Original languageEnglish
Pages (from-to)4384-4425
Number of pages42
JournalJournal of Pure and Applied Algebra
Issue number10
StatePublished - 1 Oct 2019


  • Classical groups
  • Representation zeta functions
  • Representations of compact p-adic groups

ASJC Scopus subject areas

  • Algebra and Number Theory


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