{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EPIDUZWVZFPKU72E6DJGU3L47F","short_pith_number":"pith:EPIDUZWV","schema_version":"1.0","canonical_sha256":"23d03a66d5c95eaa7f44f0d26a6d7cf96794dde0e5fadbf889d9d6c1bde1f1ba","source":{"kind":"arxiv","id":"1605.08545","version":5},"attestation_state":"computed","paper":{"title":"Geometric conditions for $\\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alberto Minguez, Erez Lapid","submitted_at":"2016-05-27T08:55:07Z","abstract_excerpt":"Let $\\pi$ be an irreducible, complex, smooth representation of $GL_n$ over a local non-archimedean (skew) field. Assuming $\\pi$ has regular Zelevinsky parameters, we give a geometric necessary and sufficient criterion for the irreducibility of the parabolic induction of $\\pi\\otimes\\pi$ to $GL_{2n}$. The latter irreducibility property is the $p$-adic analogue of a special case of the notion of \"real representations\" introduced by Leclerc and studied recently by Kang-Kashiwara-Kim-Oh (in the context of KLR or quantum affine algebras). Our criterion is in terms of singularities of Schubert variet"},"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":"1605.08545","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-27T08:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"73439270613ac727646b9e535f523ee88747c361a72241059db19db438e49b7b","abstract_canon_sha256":"15b39c4879add05c2014547746b2362d17430219ff24d0520c9304811bfcb91d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.824853Z","signature_b64":"oV6VRPCSkSrYfvXIHmT8QTQjHVaX5H+ExyO8/o/cKLRmEg0nD7eTq+GLLY2lILPW2SeGtbInMxT0rznRxsp8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23d03a66d5c95eaa7f44f0d26a6d7cf96794dde0e5fadbf889d9d6c1bde1f1ba","last_reissued_at":"2026-05-18T00:05:00.824453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.824453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric conditions for $\\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alberto Minguez, Erez Lapid","submitted_at":"2016-05-27T08:55:07Z","abstract_excerpt":"Let $\\pi$ be an irreducible, complex, smooth representation of $GL_n$ over a local non-archimedean (skew) field. Assuming $\\pi$ has regular Zelevinsky parameters, we give a geometric necessary and sufficient criterion for the irreducibility of the parabolic induction of $\\pi\\otimes\\pi$ to $GL_{2n}$. The latter irreducibility property is the $p$-adic analogue of a special case of the notion of \"real representations\" introduced by Leclerc and studied recently by Kang-Kashiwara-Kim-Oh (in the context of KLR or quantum affine algebras). Our criterion is in terms of singularities of Schubert variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08545","kind":"arxiv","version":5},"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":"1605.08545","created_at":"2026-05-18T00:05:00.824512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08545v5","created_at":"2026-05-18T00:05:00.824512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08545","created_at":"2026-05-18T00:05:00.824512+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPIDUZWVZFPK","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPIDUZWVZFPKU72E","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPIDUZWV","created_at":"2026-05-18T12:30:12.583610+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/EPIDUZWVZFPKU72E6DJGU3L47F","json":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F.json","graph_json":"https://pith.science/api/pith-number/EPIDUZWVZFPKU72E6DJGU3L47F/graph.json","events_json":"https://pith.science/api/pith-number/EPIDUZWVZFPKU72E6DJGU3L47F/events.json","paper":"https://pith.science/paper/EPIDUZWV"},"agent_actions":{"view_html":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F","download_json":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F.json","view_paper":"https://pith.science/paper/EPIDUZWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08545&json=true","fetch_graph":"https://pith.science/api/pith-number/EPIDUZWVZFPKU72E6DJGU3L47F/graph.json","fetch_events":"https://pith.science/api/pith-number/EPIDUZWVZFPKU72E6DJGU3L47F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F/action/storage_attestation","attest_author":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F/action/author_attestation","sign_citation":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F/action/citation_signature","submit_replication":"https://pith.science/pith/EPIDUZWVZFPKU72E6DJGU3L47F/action/replication_record"}},"created_at":"2026-05-18T00:05:00.824512+00:00","updated_at":"2026-05-18T00:05:00.824512+00:00"}