Regular characters of classical groups over complete discrete valuation rings

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.