{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VCHVT6XFI4H6BFARLNFNT4YHUT","short_pith_number":"pith:VCHVT6XF","schema_version":"1.0","canonical_sha256":"a88f59fae5470fe094115b4ad9f307a4ead1fa05b012d0f76caa0d6d87c3340d","source":{"kind":"arxiv","id":"1403.5132","version":1},"attestation_state":"computed","paper":{"title":"On the modular representation theory of the partition algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Armin Shalile","submitted_at":"2014-03-20T13:31:38Z","abstract_excerpt":"We determine the decomposition numbers of the partition algebra when the characteristic of the ground field is zero or larger than the degree of the partition algebra. This will allow us to determine for which exact values of the parameter the partition algebras are semisimple over an arbitrary field. Furthermore, we show that the blocks of the partition algebra over an arbitrary field categorify weight spaces of an action of type A quantum groups on an analogue of the Fock space. In particular, we recover the block structure which was recently determined by Bowman et al. In order to do so, we"},"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":"1403.5132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-20T13:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"f6dbc9aeb83c3cc81a5c7ca481aa7dd941123c9747da930ed82144bee66aee1f","abstract_canon_sha256":"556befbc6c8c87c11c2cd60dd68b0083caa6e2799f29744005ec26797cb32392"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:58.170768Z","signature_b64":"Q+LC167fzyMT5U9YweemcXv+N/83zCAQSz+R0L3OWRm8UDrAz3foZZuADK7eAYrtE57i1Q6Kg/lOALorVCfGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a88f59fae5470fe094115b4ad9f307a4ead1fa05b012d0f76caa0d6d87c3340d","last_reissued_at":"2026-05-18T02:55:58.170376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:58.170376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the modular representation theory of the partition algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Armin Shalile","submitted_at":"2014-03-20T13:31:38Z","abstract_excerpt":"We determine the decomposition numbers of the partition algebra when the characteristic of the ground field is zero or larger than the degree of the partition algebra. This will allow us to determine for which exact values of the parameter the partition algebras are semisimple over an arbitrary field. Furthermore, we show that the blocks of the partition algebra over an arbitrary field categorify weight spaces of an action of type A quantum groups on an analogue of the Fock space. In particular, we recover the block structure which was recently determined by Bowman et al. In order to do so, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5132","kind":"arxiv","version":1},"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":"1403.5132","created_at":"2026-05-18T02:55:58.170425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5132v1","created_at":"2026-05-18T02:55:58.170425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5132","created_at":"2026-05-18T02:55:58.170425+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCHVT6XFI4H6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCHVT6XFI4H6BFAR","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCHVT6XF","created_at":"2026-05-18T12:28:52.271510+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/VCHVT6XFI4H6BFARLNFNT4YHUT","json":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT.json","graph_json":"https://pith.science/api/pith-number/VCHVT6XFI4H6BFARLNFNT4YHUT/graph.json","events_json":"https://pith.science/api/pith-number/VCHVT6XFI4H6BFARLNFNT4YHUT/events.json","paper":"https://pith.science/paper/VCHVT6XF"},"agent_actions":{"view_html":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT","download_json":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT.json","view_paper":"https://pith.science/paper/VCHVT6XF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5132&json=true","fetch_graph":"https://pith.science/api/pith-number/VCHVT6XFI4H6BFARLNFNT4YHUT/graph.json","fetch_events":"https://pith.science/api/pith-number/VCHVT6XFI4H6BFARLNFNT4YHUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT/action/storage_attestation","attest_author":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT/action/author_attestation","sign_citation":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT/action/citation_signature","submit_replication":"https://pith.science/pith/VCHVT6XFI4H6BFARLNFNT4YHUT/action/replication_record"}},"created_at":"2026-05-18T02:55:58.170425+00:00","updated_at":"2026-05-18T02:55:58.170425+00:00"}