Multiplicity-freeness of Unitary Representations in Sections of Holomorphic Hilbert Bundles

Miglioli M, Neeb KH (2020)

Publication Type: Journal article

Publication year: 2020

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Book Volume: 2020

Pages Range: 4852-4889

Journal Issue: 16

DOI: 10.1093/imrn/rny160

Abstract

We prove several results asserting that the action of a Banach-Lie group on Hilbert spaces of holomorphic sections of a holomorphic Hilbert space bundle over a complex Banach manifold is multiplicity-free. These results require the existence of compatible anti-holomorphic bundle maps and certain multiplicity-freeness assumptions for stabilizer groups. For the group action on the base, the notion of an -weakly visible action (generalizing T. Koboyashi's visible actions) provides an effective way to express the assumptions in an economical fashion. In particular, we derive a version for group actions on homogeneous bundles for larger groups. We illustrate these general results by several examples related to operator groups and von Neumann algebras.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) / National Scientific and Technical Research Council AR Argentina (AR)

How to cite

APA:

Miglioli, M., & Neeb, K.H. (2020). Multiplicity-freeness of Unitary Representations in Sections of Holomorphic Hilbert Bundles. International Mathematics Research Notices, 2020(16), 4852-4889. https://doi.org/10.1093/imrn/rny160

MLA:

Miglioli, Martin, and Karl Hermann Neeb. "Multiplicity-freeness of Unitary Representations in Sections of Holomorphic Hilbert Bundles." International Mathematics Research Notices 2020.16 (2020): 4852-4889.

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