標題: | Kaehler structures on K-C/(P,P) |
作者: | Chuah, MK 應用數學系 Department of Applied Mathematics |
關鍵字: | Lie group;Kaehler;line bundle |
公開日期: | 1-八月-1997 |
摘要: | Let 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. |
URI: | http://dx.doi.org/10.1090/S0002-9947-97-01840-0 http://hdl.handle.net/11536/149602 |
ISSN: | 0002-9947 |
DOI: | 10.1090/S0002-9947-97-01840-0 |
期刊: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY |
Volume: | 349 |
起始頁: | 3373 |
結束頁: | 3390 |
顯示於類別: | 期刊論文 |