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Unipotent representations of real classical groups
Let be a complex orthogonal or complex symplectic group, and let
be a real form of , namely is a real orthogonal group, a
real symplectic group, a quaternionic orthogonal group, or a quaternionic
symplectic group. For a fixed parity , we
define a set of nilpotent
-orbits in (the Lie algebra of ). When
is the parity of the dimension of the standard module of , this is the set of the stably trivial special nilpotent orbits, which
includes all rigid special nilpotent orbits. For each , we construct all unipotent
representations of (or its metaplectic cover when is a real symplectic
group and is odd) attached to via the method of theta
lifting and show in particular that they are unitary
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