{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PVKYLSCUAEMAZFSCHM4S6WJFBH","short_pith_number":"pith:PVKYLSCU","schema_version":"1.0","canonical_sha256":"7d5585c85401180c96423b392f592509e52bf455df766a8f5c7ad5876bfb2379","source":{"kind":"arxiv","id":"1511.01381","version":3},"attestation_state":"computed","paper":{"title":"On the Stability and Gelfand Property of Symmetric Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shachar Carmeli","submitted_at":"2015-11-04T16:19:11Z","abstract_excerpt":"A symmetric pair of reductive groups $(G,H,\\theta)$ is called stable, if every closed double coset of $H$ in $G$ is preserved by the anti-involution $g\\mapsto \\theta(g^{-1})$.\n  In this paper, we develop a method to verify the stability of symmetric pairs over local fields of characteristic 0 (Archimedean and $p$-adic), using non-abelian group cohomology. Combining our method with results of Aizenbud and Gourevitch, we classify the Gelfand pairs among the pairs \\begin{align*} &(SL_n(F), (GL_k(F) \\times GL_{n - k}(F)) \\cap SL_n(F)), (U(B_1 \\oplus B_2),U(B_1) \\times U(B_2)),\\\\ &(GL_n(F),O(B)), ("},"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":"1511.01381","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-04T16:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"1406e5158f2a7434313b7a4f14416a606b8a429f1a4eee375d91e63937901861","abstract_canon_sha256":"a2fe5858d482cb2ab41bf70823ba4cd9db7c641da137642b784d04d1d717563c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:47.370797Z","signature_b64":"38uASChlRWlLtkeRBlVeyVuvDcAeq4cSDqQlD083xFkotGBxd4iyRizlzXl6yuWwmEIEzj/C28QwCsCyMO2uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d5585c85401180c96423b392f592509e52bf455df766a8f5c7ad5876bfb2379","last_reissued_at":"2026-05-17T23:41:47.370010Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:47.370010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Stability and Gelfand Property of Symmetric Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shachar Carmeli","submitted_at":"2015-11-04T16:19:11Z","abstract_excerpt":"A symmetric pair of reductive groups $(G,H,\\theta)$ is called stable, if every closed double coset of $H$ in $G$ is preserved by the anti-involution $g\\mapsto \\theta(g^{-1})$.\n  In this paper, we develop a method to verify the stability of symmetric pairs over local fields of characteristic 0 (Archimedean and $p$-adic), using non-abelian group cohomology. Combining our method with results of Aizenbud and Gourevitch, we classify the Gelfand pairs among the pairs \\begin{align*} &(SL_n(F), (GL_k(F) \\times GL_{n - k}(F)) \\cap SL_n(F)), (U(B_1 \\oplus B_2),U(B_1) \\times U(B_2)),\\\\ &(GL_n(F),O(B)), ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01381","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.01381","created_at":"2026-05-17T23:41:47.370153+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.01381v3","created_at":"2026-05-17T23:41:47.370153+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01381","created_at":"2026-05-17T23:41:47.370153+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVKYLSCUAEMA","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVKYLSCUAEMAZFSC","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVKYLSCU","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH","json":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH.json","graph_json":"https://pith.science/api/pith-number/PVKYLSCUAEMAZFSCHM4S6WJFBH/graph.json","events_json":"https://pith.science/api/pith-number/PVKYLSCUAEMAZFSCHM4S6WJFBH/events.json","paper":"https://pith.science/paper/PVKYLSCU"},"agent_actions":{"view_html":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH","download_json":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH.json","view_paper":"https://pith.science/paper/PVKYLSCU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.01381&json=true","fetch_graph":"https://pith.science/api/pith-number/PVKYLSCUAEMAZFSCHM4S6WJFBH/graph.json","fetch_events":"https://pith.science/api/pith-number/PVKYLSCUAEMAZFSCHM4S6WJFBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH/action/storage_attestation","attest_author":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH/action/author_attestation","sign_citation":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH/action/citation_signature","submit_replication":"https://pith.science/pith/PVKYLSCUAEMAZFSCHM4S6WJFBH/action/replication_record"}},"created_at":"2026-05-17T23:41:47.370153+00:00","updated_at":"2026-05-17T23:41:47.370153+00:00"}