ON RESOLVING THE MULTIPLICITY OF THE BRANCHING RULE GL(2K, C)DOWN-ARROW-SP(2K, C)

Authors
LEUNG EY
Citation
Ey. Leung, ON RESOLVING THE MULTIPLICITY OF THE BRANCHING RULE GL(2K, C)DOWN-ARROW-SP(2K, C), Journal of physics. A, mathematical and general, 27(8), 1994, pp. 2749-2760
Citations number
16
Categorie Soggetti
Physics
Journal title
Journal of physics. A, mathematical and general → ACNP
ISSN journal
03054470
Volume
27
Issue
8
Year of publication
1994
Pages
2749 - 2760
Database
ISI
SICI code
0305-4470(1994)27:8<2749:ORTMOT>2.0.ZU;2-4
Abstract
We consider the multiplicity problem of the branching rule GL(2k, C) d own Sp(2k, C). Finite-dimensional irreducible representations of GL(2k , C) are realized as right translations on subspaces of the holomorphi c Hilbert (Bargmann) spaces of q x 2k complex variables. Maps are exhi bited which carry an irreducible representation of Sp(2k, C) into thes e subspaces. An algebra of commuting operators is constructed and it i s shown how eigen-values of certain of these operators can be used to resolve the multiplicity.