{"paper":{"title":"The branching problem for generalized Verma modules, with application to the pair $(so(7),Lie G_2)$, extended version with tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Petr Somberg, Todor Milev","submitted_at":"2012-09-18T14:11:16Z","abstract_excerpt":"We discuss the branching problem for generalized Verma modules $M_\\lambda(\\mathfrak g, \\mathfrak p)$ applied to couples of reductive Lie algebras $\\bar{\\mathfrak g}\\hookrightarrow \\mathfrak g$. The analysis is based on projecting character formulas to quantify the branching, and on the action of the center of $U(\\bar{\\mathfrak g})$ to explicitly construct singular vectors realizing part of the branching. We demonstrate the results on the pair $\\mathrm{Lie}G_2\\hookrightarrow{so(7)}$ for both strongly and weakly compatible with $i(\\mathrm {Lie} G_2)$ parabolic subalgebras and a large class of in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3970","kind":"arxiv","version":3},"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"}