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dc.contributor.authorChuah, MKen_US
dc.date.accessioned2019-04-02T05:59:47Z-
dc.date.available2019-04-02T05:59:47Z-
dc.date.issued1997-08-01en_US
dc.identifier.issn0002-9947en_US
dc.identifier.urihttp://dx.doi.org/10.1090/S0002-9947-97-01840-0en_US
dc.identifier.urihttp://hdl.handle.net/11536/149602-
dc.description.abstractLet K be a compact connected semi-simple Lie group, let G = K-C, and let G = KAN be an Iwasawa decomposition. To a given K-invariant Kaehler structure omega on G/N, there corresponds a pre-quantum line bundle L on G/N. Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections O(L) as a K-representation space. We defined a K-invariant L-2-structure on O(L), and let H-omega subset of O(L) denote the space of square-integrable holomorphic sections. Then H-omega is a unitary K-representation space, but not all unitary irreducible K-representations occur as subrepresentations of H-omega. This paper serves as a continuation of that work, by generalizing the space considered. Let B be a Borel subgroup containing N, with commutator subgroup (B, B) = N. Instead of working with G/N = G/(B, B), we consider G/(P, P), for all parabolic subgroups P containing B. We carry out a similar construction, and recover in H-omega the unitary irreducible K-representations previously missing. As a result, we use these holomorphic sections to construct a model for K: a unitary K-representation in which every irreducible K-representation occurs with multiplicity one.en_US
dc.language.isoen_USen_US
dc.subjectLie groupen_US
dc.subjectKaehleren_US
dc.subjectline bundleen_US
dc.titleKaehler structures on K-C/(P,P)en_US
dc.typeArticleen_US
dc.identifier.doi10.1090/S0002-9947-97-01840-0en_US
dc.identifier.journalTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETYen_US
dc.citation.volume349en_US
dc.citation.spage3373en_US
dc.citation.epage3390en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:A1997XP80200013en_US
dc.citation.woscount8en_US
Appears in Collections:Articles