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Geometric representation theory for unitary groups of operator algebras

Daniel Beltiţă·Tudor S. Ratiu
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Abstract

Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such realizations in spaces of holomorphic sections, a class of complex coadjoint orbits of the corresponding real Banach-Lie groups are described and some homogeneous holomorphic Hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed.

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Daniel Beltiţă, Tudor S. Ratiu. 2005-01-05. Geometric representation theory for unitary groups of operator algebras. https://arxiv.org/abs/math/0501057

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