Wave front sets of reductive Lie group representations II

Harris, Brian

doi:10.1090/tran/7282

Cited by 4 publications

(1 citation statement)

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“…In the second part, the wave front set of representations plays a central role. Our argument is partly similar to [HHO16,Har18,HW17], but requires some new ingredients. It was proved in [HW17, Theorem 2.1] that the wave front set of L 2 (G R /H 0 ) equals the image of moment map.…”

Section: Note Thatmentioning

confidence: 64%

On the asymptotic support of Plancherel measures for homogeneous spaces

Harris¹,

Oshima²

2022

Preprint

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Let G be a real linear reductive group and let H be a unimodular, locally algebraic subgroup. Let supp L 2 (G/H) be the set of irreducible unitary representations of G contributing to the decomposition of L 2 (G/H), namely the support of the Plancherel measure. In this paper, we will relate supp L 2 (G/H) with the image of moment map from the cotangent bundleFor the homogeneous space X = G/H, we attach a complex Levi subgroup L X of the complexification of G and we show that in some sense "most" of representations in supp L 2 (G/H) are obtained as quantizations of coadjoint orbits O such that O ≃ G/L and that the complexification of L is conjugate to L X . Moreover, the union of such coadjoint orbits O coincides asymptotically with the moment map image. As a corollary, we show that L 2 (G/H) has a discrete series if the moment map image contains a nonempty subset of elliptic elements.2010 Mathematics Subject Classification. 22E46.

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Section: Note Thatmentioning

confidence: 64%