{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:2PY5RHGGPTJOE6NRSK5B7VIOTC","short_pith_number":"pith:2PY5RHGG","schema_version":"1.0","canonical_sha256":"d3f1d89cc67cd2e279b192ba1fd50e9886469bdcb8e70455111abcce6f931bfb","source":{"kind":"arxiv","id":"math/9809112","version":2},"attestation_state":"computed","paper":{"title":"On the Schwartz space of the basic affine space","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Braverman, David Kazhdan","submitted_at":"1998-09-20T20:29:04Z","abstract_excerpt":"Let G be the group of points of a split reductive algebraic group over a local field k and let X=G/U where U is a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of S(X) invariant under the Iwahori subgroup of G coincides with space generated by the elements of the so called periodic Lusztig's basis, introduced recently by G.Lusztig. We also give an interpretation of this "},"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":"math/9809112","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-09-20T20:29:04Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6f6e3a8e4c4b47c9bded839400b3ac075bc27ae33bea59a645268a5738cad3bc","abstract_canon_sha256":"0a550b7bd2c153f2013e53e0f97c7015a5d00e4d64e25418cb874b9199cc56fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.778666Z","signature_b64":"ybo8tyN/76cQxBRyiMG+2NI2EsD8m+QFAtwxy4uT0YDOf7gfA5UiJBkd9jOz9tdAszpdOraI7fxonu232UyoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3f1d89cc67cd2e279b192ba1fd50e9886469bdcb8e70455111abcce6f931bfb","last_reissued_at":"2026-05-18T01:05:33.777907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.777907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Schwartz space of the basic affine space","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Braverman, David Kazhdan","submitted_at":"1998-09-20T20:29:04Z","abstract_excerpt":"Let G be the group of points of a split reductive algebraic group over a local field k and let X=G/U where U is a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of S(X) invariant under the Iwahori subgroup of G coincides with space generated by the elements of the so called periodic Lusztig's basis, introduced recently by G.Lusztig. We also give an interpretation of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809112","kind":"arxiv","version":2},"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":"math/9809112","created_at":"2026-05-18T01:05:33.778032+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9809112v2","created_at":"2026-05-18T01:05:33.778032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9809112","created_at":"2026-05-18T01:05:33.778032+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PY5RHGGPTJO","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PY5RHGGPTJOE6NR","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PY5RHGG","created_at":"2026-05-18T12:25:49.038998+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/2PY5RHGGPTJOE6NRSK5B7VIOTC","json":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC.json","graph_json":"https://pith.science/api/pith-number/2PY5RHGGPTJOE6NRSK5B7VIOTC/graph.json","events_json":"https://pith.science/api/pith-number/2PY5RHGGPTJOE6NRSK5B7VIOTC/events.json","paper":"https://pith.science/paper/2PY5RHGG"},"agent_actions":{"view_html":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC","download_json":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC.json","view_paper":"https://pith.science/paper/2PY5RHGG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9809112&json=true","fetch_graph":"https://pith.science/api/pith-number/2PY5RHGGPTJOE6NRSK5B7VIOTC/graph.json","fetch_events":"https://pith.science/api/pith-number/2PY5RHGGPTJOE6NRSK5B7VIOTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC/action/storage_attestation","attest_author":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC/action/author_attestation","sign_citation":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC/action/citation_signature","submit_replication":"https://pith.science/pith/2PY5RHGGPTJOE6NRSK5B7VIOTC/action/replication_record"}},"created_at":"2026-05-18T01:05:33.778032+00:00","updated_at":"2026-05-18T01:05:33.778032+00:00"}