 |
|
|
|
| HAL: hal-00366245, version 1 |
| arXiv: 0903.1187 |
| Detailed view |  Export this paper |
|
|
|
|
| Geometric Invariant Theory and Generalized Eigenvalue Problem II |
|
|
| Nicolas Ressayre 1 |
|
|
| (2009-03-06) |
|
|
|
| Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat{G}$. Fix maximal tori and Borel subgroups of $G$ and $\hat{G}$. Consider the cone $LR^\circ(\hat{G},G)$ generated by the pairs $(\nu,\hat{\nu})$ of strictly dominant characters such that $V_\nu$ is a submodule of $V_{\hat\nu}$. The main result of this article is a bijective parametrisation of the faces of $LR^\circ(\hat G,G)$. We also explain when such a face is contained in another one. In way, we obtain results about the faces of the Dolgachev-Hu's $G$-ample cone. We also apply our results to reprove known results about the moment polytopes. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
|
|
|
CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Algebraic Geometry |
|
|
| Horn problem |
|
|
|
| Attached file list to this document: | ||||||||||
|
||||||||||
|
|
|
| hal-00366245, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00366245 | |
| oai:hal.archives-ouvertes.fr:hal-00366245 | |
| From: Nicolas Ressayre | |
| Submitted on: Friday, 6 March 2009 11:56:31 | |
| Updated on: Friday, 6 March 2009 11:59:28 | |
