Abstract
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 ℓ 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 ℓ /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 language | English |
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Pages (from-to) | 4384-4425 |
Number of pages | 42 |
Journal | Journal of Pure and Applied Algebra |
Volume | 223 |
Issue number | 10 |
DOIs | |
State | Published - 1 Oct 2019 |
Keywords
- Classical groups
- Representation zeta functions
- Representations of compact p-adic groups
ASJC Scopus subject areas
- Algebra and Number Theory