2006 Fiscal Year Final Research Report Summary
Stein extensions of symmetric spaces and the orbit correspondence on flag manifolds
| Project/Area Number |
17540074
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
MATSUKI Toshihiko Kyoto University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (20157283)
|
|---|
| Project Period (FY) |
2005 – 2006
|
| Keywords | symmetric spaces / Lie groups / representation theory |
|---|
| Research Abstract |
1. It is known that we get a convex set as the image of the compact symmetric subspace or the compactly causal symmetric subspace by the Iwasawa projection in the complexified symmetric space G_C/K_C. We showed that the image contains a neighborhood of the origin for other real symmetric subspaces of G_C/K_C.
2. S. Gindikin showed that the horospherical Cauchy transform gave an isomorphism between the space of Sato's hyperfunctions on compact symmetric spaces and the space of holomorphic functions on a convex domain. We clarified a part of his geometric idea.
3. We computed the simplest rank-two example SU(3)/SO(3) and investigated topological properties of the intersection of cycles (for integration) for the dual horospherical Cauchy transform with the convex domain obtained as the image of the horospherical Cauchy transform.
4. We investigated the action of the center on the fundamental cell for twisted conjugacy classes on compact Lie groups. Then we got a simple classification of exterior involutions on compact Lie groups.
5. We invited S.Gindikin, G.Olafsson and R. Stanton and discussed the Akhiezer-Gindikin domain and related representation theories.
|
