{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:IOXNJPCLAUHLAOVUAVWPUOGIJW","short_pith_number":"pith:IOXNJPCL","schema_version":"1.0","canonical_sha256":"43aed4bc4b050eb03ab4056cfa38c84d82e442dae68742b5625378145763e550","source":{"kind":"arxiv","id":"2404.00760","version":1},"attestation_state":"computed","paper":{"title":"Modularity for $\\mathcal{W}$-algebras and affine Springer fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Dan Xie, Peng Shan, WenBin Yan","submitted_at":"2024-03-31T18:12:05Z","abstract_excerpt":"We construct a bijection between admissible representations for an affine Lie algebra $\\mathfrak{g}$ at boundary admissible levels and $\\mathbb{C}^\\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual affine Lie algebra $\\mathfrak{g}^\\vee$. Using this bijection, we relate the modularity of the characters of admissible representations to Cherednik's Verlinde algebra construction coming from double affine Hecke algebras. Finally, we show that the expected behaviors of simple modules under quantized Drinfeld-Sokolov reductions are compatible with the reduction"},"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":"2404.00760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T18:12:05Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"title_canon_sha256":"9ba2db6b2fbc5864fbf0fb6687c64ca6d78d7f0725e9c6e00a23e78a0c596fe3","abstract_canon_sha256":"efb98b4530c1f3fe6358bb07c7c626340e1a06a0d9a582740f9e789418d495e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:03:12.114453Z","signature_b64":"WKarvJqvooYKSijkVPI80u1CHLF+Q5jCYIwO3uXXwBOD5ly/xn5k92LgLhcUltaRa/4Ws0jma0+UiLhsTFwcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43aed4bc4b050eb03ab4056cfa38c84d82e442dae68742b5625378145763e550","last_reissued_at":"2026-07-05T08:03:12.114007Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:03:12.114007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modularity for $\\mathcal{W}$-algebras and affine Springer fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Dan Xie, Peng Shan, WenBin Yan","submitted_at":"2024-03-31T18:12:05Z","abstract_excerpt":"We construct a bijection between admissible representations for an affine Lie algebra $\\mathfrak{g}$ at boundary admissible levels and $\\mathbb{C}^\\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual affine Lie algebra $\\mathfrak{g}^\\vee$. Using this bijection, we relate the modularity of the characters of admissible representations to Cherednik's Verlinde algebra construction coming from double affine Hecke algebras. Finally, we show that the expected behaviors of simple modules under quantized Drinfeld-Sokolov reductions are compatible with the reduction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00760","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00760/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2404.00760","created_at":"2026-07-05T08:03:12.114061+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.00760v1","created_at":"2026-07-05T08:03:12.114061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00760","created_at":"2026-07-05T08:03:12.114061+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOXNJPCLAUHL","created_at":"2026-07-05T08:03:12.114061+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOXNJPCLAUHLAOVU","created_at":"2026-07-05T08:03:12.114061+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOXNJPCL","created_at":"2026-07-05T08:03:12.114061+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.29921","citing_title":"Modular invariance of characters of quasi-lisse vertex algebras","ref_index":83,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04668","citing_title":"Classification of the irreducible ordinary modules for affine vertex operator superalgebras","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW","json":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW.json","graph_json":"https://pith.science/api/pith-number/IOXNJPCLAUHLAOVUAVWPUOGIJW/graph.json","events_json":"https://pith.science/api/pith-number/IOXNJPCLAUHLAOVUAVWPUOGIJW/events.json","paper":"https://pith.science/paper/IOXNJPCL"},"agent_actions":{"view_html":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW","download_json":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW.json","view_paper":"https://pith.science/paper/IOXNJPCL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.00760&json=true","fetch_graph":"https://pith.science/api/pith-number/IOXNJPCLAUHLAOVUAVWPUOGIJW/graph.json","fetch_events":"https://pith.science/api/pith-number/IOXNJPCLAUHLAOVUAVWPUOGIJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW/action/storage_attestation","attest_author":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW/action/author_attestation","sign_citation":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW/action/citation_signature","submit_replication":"https://pith.science/pith/IOXNJPCLAUHLAOVUAVWPUOGIJW/action/replication_record"}},"created_at":"2026-07-05T08:03:12.114061+00:00","updated_at":"2026-07-05T08:03:12.114061+00:00"}