Regular characters of classical groups over complete discrete valuation rings

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Shechter, Shai¹ 

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

关键词: Representations of compact p-adic groups;    Representation zeta functions;    Classical groups;   

DOI  :  10.1016/j.jpaa.2019.01.013

来源: Elsevier

【 摘 要 】

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 is an element of 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) similar or equal to 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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free