{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:3CX7YDGGY5OFS4NBNI6CLBLHG6","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":"e125ea208dd0b1ca3356b4d44a8d4c148d135aab2b9d0d280a54da29b94cd831","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2007-08-19T05:24:47Z","title_canon_sha256":"889680d05e04ade40bab7031dcae2c812e85ae6ca184474522d1fb8b4a324bcf"},"schema_version":"1.0","source":{"id":"0708.2525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2525","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2525v2","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2525","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"3CX7YDGGY5OF","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3CX7YDGGY5OFS4NB","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3CX7YDGG","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:c388de528a7418d7e9425fa697588ac68f0e8bdabad1b6b0af2ca6edd73c46f8","target":"graph","created_at":"2026-05-18T04:19:32Z","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":"In this paper, we investigate the structure and representations of the quantum group ${\\mathbf{U}(\\infty)}=\\mathbf U_\\upsilon(\\frak{gl}_\\infty)$. We will present a realization for $\\mathbf{U}(\\infty)$, following Beilinson--Lusztig--MacPherson (BLM) \\cite{BLM}, and show that the natural algebra homomorphism $\\zeta_r$ from $\\mathbf{U}(\\infty)$ to the infinite $q$-Schur algebra ${\\boldsymbol{\\mathcal S}}(\\infty,r)$ is not surjective for any $r\\geq 1$. We will give a BLM type realization for the image $\\mathbf{U}(\\infty,r):=\\zeta_r(\\mathbf{U}(\\infty))$ and discuss its presentation in terms of gene","authors_text":"Jie Du, Qiang Fu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2007-08-19T05:24:47Z","title":"Quantum $\\frak {gl}_\\infty$, infinite $q$-Schur algebras and their representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2525","kind":"arxiv","version":2},"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:a55bcc24775e645c451dff3de2b410f09ac3c08a094484dce8ab060bb7674299","target":"record","created_at":"2026-05-18T04:19:32Z","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":"e125ea208dd0b1ca3356b4d44a8d4c148d135aab2b9d0d280a54da29b94cd831","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2007-08-19T05:24:47Z","title_canon_sha256":"889680d05e04ade40bab7031dcae2c812e85ae6ca184474522d1fb8b4a324bcf"},"schema_version":"1.0","source":{"id":"0708.2525","kind":"arxiv","version":2}},"canonical_sha256":"d8affc0cc6c75c5971a16a3c258567379aee9e483e21a922f3da4e8769c97f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8affc0cc6c75c5971a16a3c258567379aee9e483e21a922f3da4e8769c97f72","first_computed_at":"2026-05-18T04:19:32.476373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:32.476373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oRpk+hAIdobIwHsb4r2TfY2bMab/f9Ul9yJNUVrWofdXu5ImAMmR0oTwudFfIQ8lID9GyOVTVsZ/1F4N2aVqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:32.476754Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a55bcc24775e645c451dff3de2b410f09ac3c08a094484dce8ab060bb7674299","sha256:c388de528a7418d7e9425fa697588ac68f0e8bdabad1b6b0af2ca6edd73c46f8"],"state_sha256":"69cdc4b1a80087ebd0599bd69c59bd9265d58ba69954468504bb60cedde5f53a"}