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We determine the closure relation among nilpotent coadjoint orbits in the dual of Lie algebras of type $B,C,F_4$ in characteristic $2$ and in the dual of Lie algebra of type $G_2$ in characteristic $3$. In each case we give an explicit description of the nilpotent pieces in the dual defined in \\cite{CP}, which are in general unions of nilpotent coadjoint orbits, coincide with the earlier case"},"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":"1112.2399","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-11T20:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"8f97813aa8c9698b13dfc8a95e430e66cff3699274ad0e19d5023f016aa2577f","abstract_canon_sha256":"5a365418bbce694a2ad71a2029a446e4011185321bfeac21736e14a4856bc16e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:05.935546Z","signature_b64":"JyQQ6DyIgw14We8W37ebEavaqf1fIS3XCNmiOELZmiyHwyRSBVHP99Y3/Buvvsspo5+vxw+CMdI54LWmGVBhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b21665863c0e352381578e53398cfd181fb291a0b99ec535c52edbc76a60c385","last_reissued_at":"2026-05-18T00:15:05.934970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:05.934970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nilpotent coadjoint orbits in small characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ting Xue","submitted_at":"2011-12-11T20:51:22Z","abstract_excerpt":"We show that the numbers of nilpotent coadjoint orbits in the dual of exceptional Lie algebra $G_2$ in characteristic $3$ and in the dual of exceptional Lie algebra $F_4$ in characteristic $2$ are finite. We determine the closure relation among nilpotent coadjoint orbits in the dual of Lie algebras of type $B,C,F_4$ in characteristic $2$ and in the dual of Lie algebra of type $G_2$ in characteristic $3$. 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