Journal of Nonlinear Mathematical Physics

Volume 6, Issue 2, May 1999, Pages 161 - 180

Representations of the Infinite Unitary Group from Constrained Quantization

Authors
N.P. LANDSMAN
Corresponding Author
N.P. LANDSMAN
Available Online 1 May 1999.
DOI
https://doi.org/10.2991/jnmp.1999.6.2.4How to use a DOI?
Abstract
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group U0(H) of all unitary operators U on a separable Hilbert space H for which U - I is compact, originally found by Kirillov and Ol'shanskii, through constrained quantization of its coadjoint orbits. For this purpose the coadjoint orbits are realized as Marsden-Weinstein quotients. The unconstrained system, given as a Weinstein dual pair, is quantized by a corresponding Howe dual pair. Constrained quantization is then performed in replacing the classical procedure of symplectic reduction by the C algebraic method of Rieffel induction. Reduction and induction have to be performed with respect to either U(M), which is straightforward, or U(M, N). In the latter case one induces from holomorphic discrete series representations, and the desired result is obtained if one ignores half-forms, and induces from a representation, `half' of whose highest weight is shifted relative to the naive orbit correspondence. This is only possible when H is finite-dimensional.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 2
Pages
161 - 180
Publication Date
1999/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.2.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - N.P. LANDSMAN
PY  - 1999
DA  - 1999/05
TI  - Representations of the Infinite Unitary Group from Constrained Quantization
JO  - Journal of Nonlinear Mathematical Physics
SP  - 161
EP  - 180
VL  - 6
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.2.4
DO  - https://doi.org/10.2991/jnmp.1999.6.2.4
ID  - LANDSMAN1999
ER  -