Invariant measures on nilpotent orbits associated with holomorphic discrete series

Božičević, Mladen

doi:10.1090/ert/580

Invariant measures on nilpotent orbits associated with holomorphic discrete series
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by Mladen Božičević

Represent. Theory 25 (2021), 732-747

DOI: https://doi.org/10.1090/ert/580

Published electronically: August 18, 2021

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Abstract:

Let $G_\mathbb R$ be a real form of a complex, semisimple Lie group $G$. Assume $G_\mathbb R$ has holomorphic discrete series. Let $\mathcal W$ be a nilpotent coadjoint $G_\mathbb R$-orbit contained in the wave front set of a holomorphic discrete series. We prove a limit formula, expressing the canonical measure on $\mathcal W$ as a limit of canonical measures on semisimple coadjoint orbits, where the parameter of orbits varies over the positive chamber defined by the Borel subalgebra associated with holomorphic discrete series.

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