Equivalence of domains arising from duality of orbits on flag manifolds
| dc.creator | Matsuki, Toshihiko | |
| dc.date | 2003-09-19 | |
| dc.date | 2004-07-30 | |
| dc.date.accessioned | 2026-07-07T06:30:08Z | |
| dc.date.available | 2026-07-07T06:30:08Z | |
| dc.description | In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type by computing many examples. In this paper, we first prove (in Theorem 1.3 and Corollary 1.4) this conjecture for the open K_C-orbit S on an ``arbitrary'' flag manifold generalizing the result of Barchini. This conjecture for closed S was solved in [WZ1], [WZ2] (Hermitian cases) and [FH] (non-Hermitian cases). We also deduce an alternative proof of this result for non-Hermitian cases from Theorem 1.3. | |
| dc.description | 32 pages; improved many arguments, also updated Remark 1.6 | |
| dc.identifier | https://arxiv.org/abs/math/0309314 | |
| dc.identifier | http://arxiv.org/abs/math/0309314 | |
| dc.identifier | Trans. Amer. Math. Soc. 358 (2006), 2217--2245. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98269 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M15; 22E15; 22E46; 32M05 | |
| dc.title | Equivalence of domains arising from duality of orbits on flag manifolds | |
| dc.type | text |