Abstract
If G is a Lie group, H⊂G is a closed subgroup, and τ is a unitary representation of H, then the authors give a sufficient condition on ξ∈ig∗ to be in the wave front set of IndHGτ. In the special case where τ is the trivial representation, this result was conjectured by Howe. If G is a real, reductive algebraic group and π is a unitary representation of G that is weakly contained in the regular representation, then the authors give a geometric description of WF(π) in terms of the direct integral decomposition of π into irreducibles. Special cases of this result were previously obtained by Kashiwara–Vergne, Howe, and Rossmann. The authors give applications to harmonic analysis problems and branching problems.
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