{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KKNQATZ6XUXUJFEQJVUGN4QYXQ","short_pith_number":"pith:KKNQATZ6","schema_version":"1.0","canonical_sha256":"529b004f3ebd2f4494904d6866f218bc01c940a85f0fe4f72c5eabe5e60467ea","source":{"kind":"arxiv","id":"1408.6790","version":1},"attestation_state":"computed","paper":{"title":"On Symplectic Periods for Inner forms of ${\\rm GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Mahendra Kumar Verma","submitted_at":"2014-08-28T17:34:28Z","abstract_excerpt":"In this paper we study the question of determining when an irreducible admissible representation of ${\\rm GL}_n(D)$ admits a symplectic model, that is when such a representation has a linear functional invariant under ${\\rm Sp}_n(D)$, where $D$ is a quaternion division algebra over a non-Archimedian local field $k$ and ${\\rm Sp}_{n}(D)$ is the unique non-split inner form of the symplectic group ${\\rm Sp}_{2n}(k)$. We show that if a representation has a symplectic model it is necessarily unique. For ${\\rm GL}_2(D)$ we completely classify those representations which have a symplectic model. Glob"},"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":"1408.6790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-28T17:34:28Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0d08c2ae4ef64c3dffe9ba5d9319d6d0c060dc7c88dc1772dd0e82b250b36124","abstract_canon_sha256":"943e87b639442537a6fb6e93ef5ddb654ff61bbbd0daa905379d128c2533215b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:00.868919Z","signature_b64":"3kHkdslyRr/97svtxaipFmIudFAhkc4fnCuCGOTAh1jyqp8PQmN8EhJMM1rI+AQL3W2I0OM4ogkyIZt7/K5gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"529b004f3ebd2f4494904d6866f218bc01c940a85f0fe4f72c5eabe5e60467ea","last_reissued_at":"2026-05-18T02:44:00.868506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:00.868506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Symplectic Periods for Inner forms of ${\\rm GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Mahendra Kumar Verma","submitted_at":"2014-08-28T17:34:28Z","abstract_excerpt":"In this paper we study the question of determining when an irreducible admissible representation of ${\\rm GL}_n(D)$ admits a symplectic model, that is when such a representation has a linear functional invariant under ${\\rm Sp}_n(D)$, where $D$ is a quaternion division algebra over a non-Archimedian local field $k$ and ${\\rm Sp}_{n}(D)$ is the unique non-split inner form of the symplectic group ${\\rm Sp}_{2n}(k)$. We show that if a representation has a symplectic model it is necessarily unique. For ${\\rm GL}_2(D)$ we completely classify those representations which have a symplectic model. Glob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6790","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":"1408.6790","created_at":"2026-05-18T02:44:00.868554+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.6790v1","created_at":"2026-05-18T02:44:00.868554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6790","created_at":"2026-05-18T02:44:00.868554+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKNQATZ6XUXU","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKNQATZ6XUXUJFEQ","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKNQATZ6","created_at":"2026-05-18T12:28:35.611951+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/KKNQATZ6XUXUJFEQJVUGN4QYXQ","json":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ.json","graph_json":"https://pith.science/api/pith-number/KKNQATZ6XUXUJFEQJVUGN4QYXQ/graph.json","events_json":"https://pith.science/api/pith-number/KKNQATZ6XUXUJFEQJVUGN4QYXQ/events.json","paper":"https://pith.science/paper/KKNQATZ6"},"agent_actions":{"view_html":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ","download_json":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ.json","view_paper":"https://pith.science/paper/KKNQATZ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.6790&json=true","fetch_graph":"https://pith.science/api/pith-number/KKNQATZ6XUXUJFEQJVUGN4QYXQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KKNQATZ6XUXUJFEQJVUGN4QYXQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ/action/storage_attestation","attest_author":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ/action/author_attestation","sign_citation":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ/action/citation_signature","submit_replication":"https://pith.science/pith/KKNQATZ6XUXUJFEQJVUGN4QYXQ/action/replication_record"}},"created_at":"2026-05-18T02:44:00.868554+00:00","updated_at":"2026-05-18T02:44:00.868554+00:00"}