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
.
