{"paper":{"title":"Bounded reductive subalgebras of sl(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexey Petukhov","submitted_at":"2010-07-08T10:39:08Z","abstract_excerpt":"Let $\\mathfrak g$ be a semisimple Lie algebra and $\\mathfrak k\\subset\\mathfrak g$ be a reductive in $\\mathfrak g$ subalgebra. A $(\\mathfrak g, \\mathfrak k)$-module is a $\\mathfrak g$-module which after restriction to $\\mathfrak k$ becomes a direct sum of finite-dimensional $\\mathfrak k$-modules. I.Penkov and V.Serganova introduce definition of bounded $(\\mathfrak g, \\mathfrak k)$-modules for reductive subalgebras $\\mathfrak k\\subset\\mathfrak g$, i.e. $(\\mathfrak g, \\mathfrak k)$-modules whose $\\mathfrak k$-multiplicities are uniformly bounded. A question arising in this context is, given $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1338","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"}