{"paper":{"title":"Support varieties of $(\\frak g, \\frak k)$-modules of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexey V. Petukhov","submitted_at":"2011-01-03T08:52:53Z","abstract_excerpt":"Let $\\frak g$ be a reductive Lie algebra over an algebraically closed field of characteristic 0 and $\\frak k$ be a reductive in $\\frak g$-subalgebra. Let $M$ be a finitely generated (possibly, infinite-dimensional) $\\frak g$-module. We say that $M$ is a $(\\frak g, \\frak k)$-module if $M$ is a direct sum of a (possibly, infinite) amount of simple finite-dimensional $\\frak k$-modules. We say that $M$ is of finite type if $M$ is a $(\\frak g, \\frak k)$-module and Hom$_\\frak k(V, M)<\\infty$ for any simple $\\frak k$-module $V$.\n  Let $X$ be a variety of all Borel subalgebras of $\\frak g$. Let $M$ be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0472","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"}