{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NNYBR2HETODJT6KXHBNGD6J3SS","short_pith_number":"pith:NNYBR2HE","schema_version":"1.0","canonical_sha256":"6b7018e8e49b8699f957385a61f93b94b4fa4415ccd7a6a181d0140904105e63","source":{"kind":"arxiv","id":"1505.04222","version":1},"attestation_state":"computed","paper":{"title":"Homomorphisms between standard modules over finite type KLR algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander S. Kleshchev, David J. Steinberg","submitted_at":"2015-05-16T00:07:25Z","abstract_excerpt":"Khovanov-Lauda-Rouquier algebras of finite Lie type come with families of standard modules, which under the Khovanov-Lauda-Rouquier categorification correspond to PBW-bases of the positive part of the corresponding quantized enveloping algebra. We show that there are no non-zero homomorphisms between distinct standard modules and all non-zero endomorphisms of a standard module are injective. We obtain applications to extensions between standard modules and modular representation theory of KLR algebras."},"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":"1505.04222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-16T00:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"e9e0d1c16e4e1b8af19bb2ea614952aebbe471d89aee2e4cca3c3f35d0bd7c71","abstract_canon_sha256":"e6e74677ea10a9d3ffa2f7cb886c06b64afd68a49d7a28b007c90e6fc6eb6030"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:13.843424Z","signature_b64":"X/gd+u7yOk71bHkij9C9rgl6jywIEro865o4dIKPJOb7Xy/IVyDuaO6slFCKlf7vgVQnEHi8ybmJ3Lr3P1hPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b7018e8e49b8699f957385a61f93b94b4fa4415ccd7a6a181d0140904105e63","last_reissued_at":"2026-05-17T23:53:13.842817Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:13.842817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphisms between standard modules over finite type KLR algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander S. Kleshchev, David J. Steinberg","submitted_at":"2015-05-16T00:07:25Z","abstract_excerpt":"Khovanov-Lauda-Rouquier algebras of finite Lie type come with families of standard modules, which under the Khovanov-Lauda-Rouquier categorification correspond to PBW-bases of the positive part of the corresponding quantized enveloping algebra. We show that there are no non-zero homomorphisms between distinct standard modules and all non-zero endomorphisms of a standard module are injective. We obtain applications to extensions between standard modules and modular representation theory of KLR algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04222","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":"1505.04222","created_at":"2026-05-17T23:53:13.842919+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04222v1","created_at":"2026-05-17T23:53:13.842919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04222","created_at":"2026-05-17T23:53:13.842919+00:00"},{"alias_kind":"pith_short_12","alias_value":"NNYBR2HETODJ","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"NNYBR2HETODJT6KX","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"NNYBR2HE","created_at":"2026-05-18T12:29:32.376354+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/NNYBR2HETODJT6KXHBNGD6J3SS","json":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS.json","graph_json":"https://pith.science/api/pith-number/NNYBR2HETODJT6KXHBNGD6J3SS/graph.json","events_json":"https://pith.science/api/pith-number/NNYBR2HETODJT6KXHBNGD6J3SS/events.json","paper":"https://pith.science/paper/NNYBR2HE"},"agent_actions":{"view_html":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS","download_json":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS.json","view_paper":"https://pith.science/paper/NNYBR2HE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04222&json=true","fetch_graph":"https://pith.science/api/pith-number/NNYBR2HETODJT6KXHBNGD6J3SS/graph.json","fetch_events":"https://pith.science/api/pith-number/NNYBR2HETODJT6KXHBNGD6J3SS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS/action/storage_attestation","attest_author":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS/action/author_attestation","sign_citation":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS/action/citation_signature","submit_replication":"https://pith.science/pith/NNYBR2HETODJT6KXHBNGD6J3SS/action/replication_record"}},"created_at":"2026-05-17T23:53:13.842919+00:00","updated_at":"2026-05-17T23:53:13.842919+00:00"}