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Invariant measures on nilpotent orbits associated with holomorphic discrete series


Author: Mladen Božičević
Journal: Represent. Theory 25 (2021), 732-747
MSC (2020): Primary 22E46; Secondary 22E30
DOI: https://doi.org/10.1090/ert/580
Published electronically: August 18, 2021
MathSciNet review: 4301562
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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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Additional Information

Mladen Božičević
Affiliation: Department of Geotechnical Engineering, University of Zagreb, Hallerova 7, 42000 Varaždin, Croatia
ORCID: 0000-0002-2588-723X
Email: mladen.bozicevic@gmail.com

Received by editor(s): January 26, 2021
Received by editor(s) in revised form: May 25, 2021
Published electronically: August 18, 2021
Additional Notes: The author was partially supported by grant no. 4176 of the Croatian Science Foundation
Article copyright: © Copyright 2021 American Mathematical Society