Journal article
Representation theory of an infinite-dimensional unitary group [Ph.D. Thesis]
Representation theory of an infinite-dimensional unitary group [Ph.D. Thesis], pp.85P-85P
01 Oct 1979
Abstract
The problem of extending the Borel-Weil realization for the irreducible representations of compact Lie groups via holomorphic induction to the infinite-dimensional group, G, of unitary operators on a separable Hiblert space is studied. A canonical equivalence between a strongly continuous irreducible unitary representation of G, Ind(f,hol), and a tensorial realization of the same representation is established when f satisfies in addition a negativity condition. It is established that any norm continuous factor representation of G is a multiple of an irreducible representation so that pi is type 1, and that the norm continuous irreducible representations are parameterized, up to unitary equivalence, by a pair of finite lists of decreasing positive integers. If the norm continuity assumption is dropped, then G admits strongly continuous type 2 sub 1 factor representations. Hence, G is not a type 1 group.
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Details
- Title
- Representation theory of an infinite-dimensional unitary group [Ph.D. Thesis]
- Creators
- R Boyer
- Publication Details
- Representation theory of an infinite-dimensional unitary group [Ph.D. Thesis], pp.85P-85P
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]; Mathematics
- Identifiers
- 991020638515704721