{"paper":{"title":"Geometric Invariant Theory and Generalized Eigenvalue Problem II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M)","submitted_at":"2009-03-06T10:59:18Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1187","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}