Generic representations of parabolic subgroups. CaseII-so(2n+l,c)

Abstract

We construct the set of generic representations for parabolic sub-groups of the complex orthogonal group SO(2n + 1C) and show that the set O _p of generic representations of an arbitrary parabolic subgroup P ⊂ S O(2n + 1, C) can be explicitly described in terms of unitary representations of some smaller reductive group G _p . More preciselyO _p is either homeomorphic to the unitary dual of G _p or can be written as a disjoint union , where h >0 and each set is homeomorphic to Ĝ _p .