{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WWFY2LXLEQK3SL5DFTFAQVUSN5","short_pith_number":"pith:WWFY2LXL","canonical_record":{"source":{"id":"1212.6505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-28T11:38:28Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ef21651f50e5207517b9daf0cf9b445f2d154fe5ab3ab1d760048304bfe63658","abstract_canon_sha256":"68808140e91394e2215b1b9ae00186a1c35dc16a34217c6917b45b6cac4e6905"},"schema_version":"1.0"},"canonical_sha256":"b58b8d2eeb2415b92fa32cca0856926f5f9f3df0b7eb40dcb34b6fcbaad919f7","source":{"kind":"arxiv","id":"1212.6505","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6505","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6505v3","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6505","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"WWFY2LXLEQK3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WWFY2LXLEQK3SL5D","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WWFY2LXL","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WWFY2LXLEQK3SL5DFTFAQVUSN5","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-28T11:38:28Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ef21651f50e5207517b9daf0cf9b445f2d154fe5ab3ab1d760048304bfe63658","abstract_canon_sha256":"68808140e91394e2215b1b9ae00186a1c35dc16a34217c6917b45b6cac4e6905"},"schema_version":"1.0"},"canonical_sha256":"b58b8d2eeb2415b92fa32cca0856926f5f9f3df0b7eb40dcb34b6fcbaad919f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:34.516109Z","signature_b64":"Gb9Lyxo8xwNaeGR/6KRTeFakfTqGKLUTEep3VznqBZmLDDhq4V/S/bLK/p5Zs0+o8uwJ7QaZLr6LgA9E6APWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58b8d2eeb2415b92fa32cca0856926f5f9f3df0b7eb40dcb34b6fcbaad919f7","last_reissued_at":"2026-05-18T03:07:34.515543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:34.515543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6505","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtWh3plnD/BAcKCJCZdA9gX3ve8fznZCDvTmrwXCrPPk8Z4T+sFvio9hJdJ/DH9jLMk18q/63rciS9pDfm8rBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T08:58:10.210927Z"},"content_sha256":"de6d1b0f8068ca835845ed7693ab27e6b6421baee0afeea130e24bae4f234dce","schema_version":"1.0","event_id":"sha256:de6d1b0f8068ca835845ed7693ab27e6b6421baee0afeea130e24bae4f234dce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WWFY2LXLEQK3SL5DFTFAQVUSN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weyl modules and Levi subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Ghislain Fourier","submitted_at":"2012-12-28T11:38:28Z","abstract_excerpt":"For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules of current algebras to this Levi subalgebra. We identify necessary and sufficient conditions on a pair of a Levi subalgebra and a dominant integral weight, such that the restricted module is a global (resp. a local) Weyl module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6505","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSRflJ0+4jK7cwP9JvZUP3mwAcSlKuCLm8JDLfVL2pcbwBKSxaBUqtHgZ+qHONGxmuAahZCLHtP7twFWGS5HBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T08:58:10.211275Z"},"content_sha256":"140c6a6d91cae3a50e959c1111392a89d8b6772557d8f8a75eff7d3db23d8817","schema_version":"1.0","event_id":"sha256:140c6a6d91cae3a50e959c1111392a89d8b6772557d8f8a75eff7d3db23d8817"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/bundle.json","state_url":"https://pith.science/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T08:58:10Z","links":{"resolver":"https://pith.science/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5","bundle":"https://pith.science/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/bundle.json","state":"https://pith.science/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWFY2LXLEQK3SL5DFTFAQVUSN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WWFY2LXLEQK3SL5DFTFAQVUSN5","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":"68808140e91394e2215b1b9ae00186a1c35dc16a34217c6917b45b6cac4e6905","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-28T11:38:28Z","title_canon_sha256":"ef21651f50e5207517b9daf0cf9b445f2d154fe5ab3ab1d760048304bfe63658"},"schema_version":"1.0","source":{"id":"1212.6505","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6505","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6505v3","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6505","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"WWFY2LXLEQK3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WWFY2LXLEQK3SL5D","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WWFY2LXL","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:140c6a6d91cae3a50e959c1111392a89d8b6772557d8f8a75eff7d3db23d8817","target":"graph","created_at":"2026-05-18T03:07:34Z","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":"For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules of current algebras to this Levi subalgebra. We identify necessary and sufficient conditions on a pair of a Levi subalgebra and a dominant integral weight, such that the restricted module is a global (resp. a local) Weyl module.","authors_text":"Ghislain Fourier","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-28T11:38:28Z","title":"Weyl modules and Levi subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6505","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:de6d1b0f8068ca835845ed7693ab27e6b6421baee0afeea130e24bae4f234dce","target":"record","created_at":"2026-05-18T03:07:34Z","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":"68808140e91394e2215b1b9ae00186a1c35dc16a34217c6917b45b6cac4e6905","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-28T11:38:28Z","title_canon_sha256":"ef21651f50e5207517b9daf0cf9b445f2d154fe5ab3ab1d760048304bfe63658"},"schema_version":"1.0","source":{"id":"1212.6505","kind":"arxiv","version":3}},"canonical_sha256":"b58b8d2eeb2415b92fa32cca0856926f5f9f3df0b7eb40dcb34b6fcbaad919f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b58b8d2eeb2415b92fa32cca0856926f5f9f3df0b7eb40dcb34b6fcbaad919f7","first_computed_at":"2026-05-18T03:07:34.515543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:34.515543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gb9Lyxo8xwNaeGR/6KRTeFakfTqGKLUTEep3VznqBZmLDDhq4V/S/bLK/p5Zs0+o8uwJ7QaZLr6LgA9E6APWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:34.516109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6505","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de6d1b0f8068ca835845ed7693ab27e6b6421baee0afeea130e24bae4f234dce","sha256:140c6a6d91cae3a50e959c1111392a89d8b6772557d8f8a75eff7d3db23d8817"],"state_sha256":"3017a8d188d26232485fc14896c2dbe710d69864c9a7bdc406444565f11c943c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oczNTaMciBhgnbEOrVyfT02BUC87ufYnimciu8lOWRVVOkB9XsaGyL2IOdU1Keqd3+ULuKpqqL90QOoQggyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T08:58:10.213944Z","bundle_sha256":"3dd090f54d0499f36dfc00679c6570dfcf39fb2a484fa8b136e99e34f11f9b22"}}