{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BX7ECSHMDCO7GPDRQDME2ZHEA3","short_pith_number":"pith:BX7ECSHM","schema_version":"1.0","canonical_sha256":"0dfe4148ec189df33c7180d84d64e406e99dad0c8c28b7c1d2501c0d205a7756","source":{"kind":"arxiv","id":"1412.0002","version":1},"attestation_state":"computed","paper":{"title":"Signature characters of highest-weight representations of $U_{q}(\\mathfrak{gl}_{n})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Vidya Venkateswaran","submitted_at":"2014-11-26T21:43:14Z","abstract_excerpt":"We consider $U_{q}(\\mathfrak{gl}_{n})$, the quantum group of type $A$ for $|q| = 1$, $q$ generic. We provide formulas for signature characters of irreducible finite-dimensional highest weight modules and Verma modules. In both cases, the technique involves combinatorics of the Gelfand-Tsetlin bases. As an application, we obtain information about unitarity of finite-dimensional irreducible representations for arbitrary $q$: we classify the continuous spectrum of the unitarity locus. We also recover some known results in the classical limit $q \\rightarrow 1$ that were obtained by different means"},"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":"1412.0002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-26T21:43:14Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"284a572d730d45e3089e410363162032240e3d144a0dc3579368b42eac51be1a","abstract_canon_sha256":"606a3ffc22510b7498097a4ac5190e87d1ed6dc95f46f500c336b9869365e81b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:31.531144Z","signature_b64":"vlQ1lVkuSE4DRsRPNo2Gvk89rem09++spMN3Xof9gS6h+cnLoxvqq6KsGvPlbBhGQAC/FMiwhu62v8AzJCkKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dfe4148ec189df33c7180d84d64e406e99dad0c8c28b7c1d2501c0d205a7756","last_reissued_at":"2026-05-18T02:32:31.530772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:31.530772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signature characters of highest-weight representations of $U_{q}(\\mathfrak{gl}_{n})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Vidya Venkateswaran","submitted_at":"2014-11-26T21:43:14Z","abstract_excerpt":"We consider $U_{q}(\\mathfrak{gl}_{n})$, the quantum group of type $A$ for $|q| = 1$, $q$ generic. We provide formulas for signature characters of irreducible finite-dimensional highest weight modules and Verma modules. In both cases, the technique involves combinatorics of the Gelfand-Tsetlin bases. As an application, we obtain information about unitarity of finite-dimensional irreducible representations for arbitrary $q$: we classify the continuous spectrum of the unitarity locus. We also recover some known results in the classical limit $q \\rightarrow 1$ that were obtained by different means"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0002","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":"1412.0002","created_at":"2026-05-18T02:32:31.530828+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0002v1","created_at":"2026-05-18T02:32:31.530828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0002","created_at":"2026-05-18T02:32:31.530828+00:00"},{"alias_kind":"pith_short_12","alias_value":"BX7ECSHMDCO7","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BX7ECSHMDCO7GPDR","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BX7ECSHM","created_at":"2026-05-18T12:28:22.404517+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/BX7ECSHMDCO7GPDRQDME2ZHEA3","json":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3.json","graph_json":"https://pith.science/api/pith-number/BX7ECSHMDCO7GPDRQDME2ZHEA3/graph.json","events_json":"https://pith.science/api/pith-number/BX7ECSHMDCO7GPDRQDME2ZHEA3/events.json","paper":"https://pith.science/paper/BX7ECSHM"},"agent_actions":{"view_html":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3","download_json":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3.json","view_paper":"https://pith.science/paper/BX7ECSHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0002&json=true","fetch_graph":"https://pith.science/api/pith-number/BX7ECSHMDCO7GPDRQDME2ZHEA3/graph.json","fetch_events":"https://pith.science/api/pith-number/BX7ECSHMDCO7GPDRQDME2ZHEA3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3/action/storage_attestation","attest_author":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3/action/author_attestation","sign_citation":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3/action/citation_signature","submit_replication":"https://pith.science/pith/BX7ECSHMDCO7GPDRQDME2ZHEA3/action/replication_record"}},"created_at":"2026-05-18T02:32:31.530828+00:00","updated_at":"2026-05-18T02:32:31.530828+00:00"}