{"paper":{"title":"Symplectic branching laws and Hermitian symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.SG"],"primary_cat":"math.RT","authors_text":"Benjamin Schwarz, Henrik Sepp\\\"anen","submitted_at":"2011-10-28T13:11:51Z","abstract_excerpt":"Let $G$ be a complex simple Lie group, and let $U \\subseteq G$ be a maximal compact subgroup. Assume that $G$ admits a homogenous space $X=G/Q=U/K$ which is a compact Hermitian symmetric space. Let $\\mathscr{L} \\rightarrow X$ be the ample line bundle which generates the Picard group of $X$. In this paper we study the restrictions to $K$ of the family $(H^0(X, \\mathscr{L}^k))_{k \\in \\N}$ of irreducible $G$-representations. We describe explicitly the moment polytopes for the moment maps $X \\rightarrow \\fk^*$ associated to positive integer multiples of the Kostant-Kirillov symplectic form on $X$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6324","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"}