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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.7982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-31T13:08:29Z","cross_cats_sorted":[],"title_canon_sha256":"dfe81e6fd599c06fa06f7d82f263c115672970241adc4c4eaf4e47d282c56b4d","abstract_canon_sha256":"0ffa8294646c5d7f7775597f711dc983a4c4228094156afe4c44ee50a0c8d890"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.218392Z","signature_b64":"T7lSnTPhJm+ooWvn2sUetlt/2O0/NAV8N9vEp4HGMDkKDCbD5hYt9XeNRTcVDnq8Bi/A1SIexboM4PEGp+IwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3de376e38eed97e02762a60914be5d80fbd75220c7b6d79b383627231209e1d","last_reissued_at":"2026-05-18T02:40:47.217855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.217855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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) $. 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