Regular characters of classical groups over complete discrete valuation rings |
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Authors: | Shai Shechter |
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Affiliation: | Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel |
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Abstract: | Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. |
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Keywords: | 20C15 20G05 11M41 Representations of compact p-adic groups Representation zeta functions Classical groups |
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