{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:UICLOX6CFAJLSASCN4V6KYGQO3","short_pith_number":"pith:UICLOX6C","schema_version":"1.0","canonical_sha256":"a204b75fc22812b902426f2be560d076e94bf2cd86019d338a6bcbabb51f12cd","source":{"kind":"arxiv","id":"hep-th/9310083","version":2},"attestation_state":"computed","paper":{"title":"Representations of affine Lie algebras, parabolic differential equations, and Lame functions","license":"","headline":"","cross_cats":["math.CA","math.QA"],"primary_cat":"hep-th","authors_text":"Alexander Kirillov Jr, Pavel Etingof","submitted_at":"1993-10-14T15:19:41Z","abstract_excerpt":"We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\\Tr (\\Phi_1 (z_1)\\ldots \\Phi_n (z_n)q^{-\\d}e^{h})$ where $\\Phi_i$ are intertwiners between Verma modules and evaluation modules over an affine Lie algebra $\\ghat$, $\\d$ is the grading operator in a Verma module and $h$ is in the Cartan subalgebra of $\\g$. We derive a system of differential equations satisfied by such a function. In particular, the calculation of $q\\frac{\\d} {\\d q} F$ yields a parabolic sec"},"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":"hep-th/9310083","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-10-14T15:19:41Z","cross_cats_sorted":["math.CA","math.QA"],"title_canon_sha256":"bb5d0ead8125573876a400a429f8e8fb276935116a42325f2cfcc991957e01ec","abstract_canon_sha256":"c89ff23bd0c20fe7a5a80fc5dbbaf8ed549bf17bd38b18377aed65871af3cc71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:04.756472Z","signature_b64":"6tT2lUhBzk6mDRinQKO+nOXAcWyJrOIAWU6Xp605IMX+MLApX1cSaizDXaaeKHmFm2cgmOgUaa3/BMB7a/0SDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a204b75fc22812b902426f2be560d076e94bf2cd86019d338a6bcbabb51f12cd","last_reissued_at":"2026-05-18T01:06:04.755787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:04.755787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of affine Lie algebras, parabolic differential equations, and Lame functions","license":"","headline":"","cross_cats":["math.CA","math.QA"],"primary_cat":"hep-th","authors_text":"Alexander Kirillov Jr, Pavel Etingof","submitted_at":"1993-10-14T15:19:41Z","abstract_excerpt":"We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\\Tr (\\Phi_1 (z_1)\\ldots \\Phi_n (z_n)q^{-\\d}e^{h})$ where $\\Phi_i$ are intertwiners between Verma modules and evaluation modules over an affine Lie algebra $\\ghat$, $\\d$ is the grading operator in a Verma module and $h$ is in the Cartan subalgebra of $\\g$. We derive a system of differential equations satisfied by such a function. In particular, the calculation of $q\\frac{\\d} {\\d q} F$ yields a parabolic sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9310083","kind":"arxiv","version":2},"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":"hep-th/9310083","created_at":"2026-05-18T01:06:04.755885+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9310083v2","created_at":"2026-05-18T01:06:04.755885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9310083","created_at":"2026-05-18T01:06:04.755885+00:00"},{"alias_kind":"pith_short_12","alias_value":"UICLOX6CFAJL","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"UICLOX6CFAJLSASC","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"UICLOX6C","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.00529","citing_title":"Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3","json":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3.json","graph_json":"https://pith.science/api/pith-number/UICLOX6CFAJLSASCN4V6KYGQO3/graph.json","events_json":"https://pith.science/api/pith-number/UICLOX6CFAJLSASCN4V6KYGQO3/events.json","paper":"https://pith.science/paper/UICLOX6C"},"agent_actions":{"view_html":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3","download_json":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3.json","view_paper":"https://pith.science/paper/UICLOX6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9310083&json=true","fetch_graph":"https://pith.science/api/pith-number/UICLOX6CFAJLSASCN4V6KYGQO3/graph.json","fetch_events":"https://pith.science/api/pith-number/UICLOX6CFAJLSASCN4V6KYGQO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3/action/storage_attestation","attest_author":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3/action/author_attestation","sign_citation":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3/action/citation_signature","submit_replication":"https://pith.science/pith/UICLOX6CFAJLSASCN4V6KYGQO3/action/replication_record"}},"created_at":"2026-05-18T01:06:04.755885+00:00","updated_at":"2026-05-18T01:06:04.755885+00:00"}