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Set $V:=\\mathfrak g_\\flat(-1)^*$ and $\\mathfrak g:=\\mathfrak g_\\flat(0)$.\n  In most cases, the space $\\mathcal P(V)$ of superpolynomials on $V$ is a completely reducible and multiplicity-free representation of $\\mathfrak g$, with a decomposition $\\mathcal P(V):=\\bigoplus_{\\lambda\\in\\Omega}V_\\lambda$, where $\\left"},"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":"1807.07340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T10:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"5790a366fb87acc37282f9c8ebddedf45204d33b355cfc82646f7dc8d99eaef6","abstract_canon_sha256":"7713fa0ea926fdb02cc62ac52bfd336fa459fc7406c29b973d269ab76770f06b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:50.928504Z","signature_b64":"1z6u8MiPr9Cas8ja19uzH39W0qgMBowv7MUGWUu2s5dho33PRcKEOsAePdtJdZ7m1vhj9JOVqWhMsTFo+OouDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f3735d873e56db4a58f161f51bf5f1f8819926c7509abbfa0596521bc5f97d0","last_reissued_at":"2026-05-17T23:48:50.927827Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:50.927827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Capelli eigenvalue problem for Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hadi Salmasian, Siddhartha Sahi, Vera Serganova","submitted_at":"2018-07-19T10:51:50Z","abstract_excerpt":"For a finite dimensional unital complex simple Jordan superalgebra $J$, the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\\mathfrak g_\\flat\\cong \\mathfrak g_\\flat(-1)\\oplus\\mathfrak g_\\flat(0)\\oplus\\mathfrak g_\\flat(1)$, such that $\\mathfrak g_\\flat(-1)\\cong J$. Set $V:=\\mathfrak g_\\flat(-1)^*$ and $\\mathfrak g:=\\mathfrak g_\\flat(0)$.\n  In most cases, the space $\\mathcal P(V)$ of superpolynomials on $V$ is a completely reducible and multiplicity-free representation of $\\mathfrak g$, with a decomposition $\\mathcal P(V):=\\bigoplus_{\\lambda\\in\\Omega}V_\\lambda$, where $\\left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07340","kind":"arxiv","version":4},"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":"1807.07340","created_at":"2026-05-17T23:48:50.927925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.07340v4","created_at":"2026-05-17T23:48:50.927925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07340","created_at":"2026-05-17T23:48:50.927925+00:00"},{"alias_kind":"pith_short_12","alias_value":"P43TLWDT4VW3","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P43TLWDT4VW3JJMP","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P43TLWDT","created_at":"2026-05-18T12:32:43.782077+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/P43TLWDT4VW3JJMPCYPVDP27D6","json":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6.json","graph_json":"https://pith.science/api/pith-number/P43TLWDT4VW3JJMPCYPVDP27D6/graph.json","events_json":"https://pith.science/api/pith-number/P43TLWDT4VW3JJMPCYPVDP27D6/events.json","paper":"https://pith.science/paper/P43TLWDT"},"agent_actions":{"view_html":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6","download_json":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6.json","view_paper":"https://pith.science/paper/P43TLWDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.07340&json=true","fetch_graph":"https://pith.science/api/pith-number/P43TLWDT4VW3JJMPCYPVDP27D6/graph.json","fetch_events":"https://pith.science/api/pith-number/P43TLWDT4VW3JJMPCYPVDP27D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/action/storage_attestation","attest_author":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/action/author_attestation","sign_citation":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/action/citation_signature","submit_replication":"https://pith.science/pith/P43TLWDT4VW3JJMPCYPVDP27D6/action/replication_record"}},"created_at":"2026-05-17T23:48:50.927925+00:00","updated_at":"2026-05-17T23:48:50.927925+00:00"}