{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZMLIIOZJG4R3DWUXKSW6L7UE6N","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":"1582bb302109130eae2eeacd930049b1f65dc0de2c531b29e03bd583f7269e67","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-29T00:24:49Z","title_canon_sha256":"1da905f74bf0b81d973a01377cd34b43057274f8dffeaa75113688010ff4c6f4"},"schema_version":"1.0","source":{"id":"1505.07891","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07891","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07891v3","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07891","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZMLIIOZJG4R3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMLIIOZJG4R3DWUX","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMLIIOZJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:e76c3f97480673e92fb568fd779538f015814b4e47673301b7cfcd74c04134c8","target":"graph","created_at":"2026-05-18T00:55:04Z","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":"We study the polynomial representation of the rational Cherednik algebra of type $A_{n-1}$ with generic parameter in characteristic $p$ for $p \\mid n$. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic $p$ analogues of existing characteristic $0$ results.","authors_text":"Sheela Devadas, Yi Sun","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-29T00:24:49Z","title":"The polynomial representation of the type $A_{n - 1}$ rational Cherednik algebra in characteristic $p \\mid n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07891","kind":"arxiv","version":3},"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:a331a64dbfadba2c903cb0b9339b33f093bf8e977ce2965cee43864ec41f95d4","target":"record","created_at":"2026-05-18T00:55:04Z","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":"1582bb302109130eae2eeacd930049b1f65dc0de2c531b29e03bd583f7269e67","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-29T00:24:49Z","title_canon_sha256":"1da905f74bf0b81d973a01377cd34b43057274f8dffeaa75113688010ff4c6f4"},"schema_version":"1.0","source":{"id":"1505.07891","kind":"arxiv","version":3}},"canonical_sha256":"cb16843b293723b1da9754ade5fe84f37cd01cb7fc368491aa3ebcb499a8670c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb16843b293723b1da9754ade5fe84f37cd01cb7fc368491aa3ebcb499a8670c","first_computed_at":"2026-05-18T00:55:04.393471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:04.393471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0dhwFq3CRcn95+zC8fksfpr+F6lHIyqlpROhnIb69nmCtTSF66VjZCf1X7GLsXvAjcgmhfdnxq5+pnV7VDjmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:04.394051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07891","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a331a64dbfadba2c903cb0b9339b33f093bf8e977ce2965cee43864ec41f95d4","sha256:e76c3f97480673e92fb568fd779538f015814b4e47673301b7cfcd74c04134c8"],"state_sha256":"f852cda8ef6aafa4481f68c6219fb139dfffdd84ab82929e964eadd4cdc1769b"}