{"paper":{"title":"Reductions for branching coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M)","submitted_at":"2011-02-01T16:05:19Z","abstract_excerpt":"Let $G$ be a connected reductive subgroup of a complex connected reductive group $\\hat{G}$. We are interested in the branching problem. Fix maximal tori and Borel subgroups of $G$ and $\\hat G$. Consider the cone $lr(G,\\hat G)$ generated by the pairs $(\\nu,\\hat nu)$ of dominant characters such that $V_\\nu^*$ is a submodule of $V_{\\hat nu}$. It is known that $lr(G,\\hat G)$ is a closed convex polyhedral cone. In this work, we show that every regular face of $lr(G,\\hat G)$ gives rise to a {\\it reduction rule} for multiplicities. More precisely, we prove that for $(\\nu,\\hat nu)$ on such a face, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0196","kind":"arxiv","version":2},"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"}