Schur-Weyl Theory for C*-algebras

Beltita D, Neeb KH (2012)

Publication Type: Journal article, Original article

Publication year: 2012

Journal

Mathematische Nachrichten Wiley-VCH Verlag

Publisher: Wiley-VCH Verlag

Book Volume: 285

Pages Range: 1170 - 1198

Journal Issue: 10

DOI: 10.1002/mana.201100114

Abstract

To each irreducible infinite dimensional representation equation image of a C*-algebra equation image, we associate a collection of irreducible norm-continuous unitary representations equation image of its unitary group equation image, whose equivalence classes are parameterized by highest weights in the same way as the irreducible bounded unitary representations of the group equation image are. These are precisely the representations arising in the decomposition of the tensor products equation image under equation image. We show that these representations can be realized by sections of holomorphic line bundles over homogeneous Kähler manifolds on which equation image acts transitively and that the corresponding norm-closed momentum sets equation image distinguish inequivalent representations of this type.

Authors with CRIS profile

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

How to cite

APA:

Beltita, D., & Neeb, K.H. (2012). Schur-Weyl Theory for C*-algebras. Mathematische Nachrichten, 285(10), 1170 - 1198. https://dx.doi.org/10.1002/mana.201100114

MLA:

Beltita, Daniel, and Karl Hermann Neeb. "Schur-Weyl Theory for C*-algebras." Mathematische Nachrichten 285.10 (2012): 1170 - 1198.

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