{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C4TSFE6QKM5EPYOUEFZ6YNMAFF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bd1f7b210f2199cb033cf2d55fe13fec04b371718ff5055824e4ab62d2bdc47b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:54:39Z","title_canon_sha256":"186fb13c783185a43a646517be83bf0eea2c9ac3b7f5858d36a0acab6f25079b"},"schema_version":"1.0","source":{"id":"1303.6815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6815","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6815v2","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6815","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"pith_short_12","alias_value":"C4TSFE6QKM5E","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C4TSFE6QKM5EPYOU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C4TSFE6Q","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:d542b7bccc8cabf9374cf2ba6b50cd2597607f9da91e91251e62aacb60482f82","target":"graph","created_at":"2026-05-18T01:12:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The classical Cartan-Helgason theorem characterises finite-dimensional spherical representations of reductive Lie groups in terms of their highest weights. We generalise the theorem to the case of a reductive symmetric supergroup pair $(G,K)$ of even type. Along the way, we compute the Harish-Chandra $c$-function of the symmetric superspace $G/K$. By way of an application, we show that all spherical representations are self-dual in type AIII|AIII.","authors_text":"Alexander Alldridge, Sebastian Schmittner","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:54:39Z","title":"Spherical representations of Lie supergroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6815","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c4435850f86e01832cf0930555eb75ec4ec1f9a5e8984477df7fcbf32c4806c4","target":"record","created_at":"2026-05-18T01:12:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bd1f7b210f2199cb033cf2d55fe13fec04b371718ff5055824e4ab62d2bdc47b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:54:39Z","title_canon_sha256":"186fb13c783185a43a646517be83bf0eea2c9ac3b7f5858d36a0acab6f25079b"},"schema_version":"1.0","source":{"id":"1303.6815","kind":"arxiv","version":2}},"canonical_sha256":"17272293d0533a47e1d42173ec3580295d727387c7c4e15b16f2c193596ac32e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17272293d0533a47e1d42173ec3580295d727387c7c4e15b16f2c193596ac32e","first_computed_at":"2026-05-18T01:12:18.998978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:18.998978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ary+y3Lo8XooXKQCPOeMdvMTit1mqFLYKHa5AoBKBbPM+cFJ6hwmAZAQsRR737TIPQO56I015XE+tVHE8ut+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:18.999349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4435850f86e01832cf0930555eb75ec4ec1f9a5e8984477df7fcbf32c4806c4","sha256:d542b7bccc8cabf9374cf2ba6b50cd2597607f9da91e91251e62aacb60482f82"],"state_sha256":"aaa772316917d49373155812046f4789e1999c56f573ff707fb3b3953e92e2cf"}