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

Miglioli M, Neeb KH (2020)


Publication Type: Journal article

Publication year: 2020

Journal

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.

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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://dx.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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