{"paper":{"title":"Codimension one connectedness of the graph of associated varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Akihito Wachi, Kyo Nishiyama, Peter Trapa","submitted_at":"2014-03-31T13:08:29Z","abstract_excerpt":"Let $ \\pi $ be an irreducible Harish-Chandra $ (\\mathfrak{g}, K) $-module, and denote its associated variety by $ AV(\\pi) $. If $ AV(\\pi) $ is reducible, then each irreducible component must contain codimension one boundary component. Thus we are interested in the codimension one adjacency of nilpotent orbits for a symmetric pair $ (G, K) $. We define the notion of orbit graph and associated graph for $ \\pi $, and study its structure for classical symmetric pairs; number of vertices, edges, connected components, etc. As a result, we prove that the orbit graph is connecetd for even nilpotent or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7982","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"}