{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:ZLKVQQ5GYPPPZDW3KX3LPXINAE","short_pith_number":"pith:ZLKVQQ5G","schema_version":"1.0","canonical_sha256":"cad55843a6c3defc8edb55f6b7dd0d013ca946245ccf06ae2d957b21fd7675a2","source":{"kind":"arxiv","id":"0912.4190","version":2},"attestation_state":"computed","paper":{"title":"Hilbert modules associated to parabolically induced representations of semisimple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.OA","authors_text":"Pierre Clare","submitted_at":"2009-12-21T15:26:41Z","abstract_excerpt":"Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing modules. Considering G to be a semisimple Lie group and H to be the Levi component L of a parabolic subgroup P=LN, the Hilbert module associated to X=G/N encodes the P-series representations of G coming from parabolic subgroups associated to P. We provide several descriptions of this Hilbert module, corresponding to the classical pictures of P-series. We then chara"},"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":"0912.4190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-12-21T15:26:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"fe518006a4bb449ab506790036d2fa2de48f5032be0244071c8053eafed97497","abstract_canon_sha256":"b6290e260efa7efd1520b2d03e8751cd3b01bcf23571f470b8d4423f444d7394"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:57.919846Z","signature_b64":"Ryv7Uw40D1l01wKtd8aJQB003SjhLuh9TJKdL9Bee2GrdPCrWAFVLVJJoX0zCw6BRMGzaWno8VsF7U9v5tY6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cad55843a6c3defc8edb55f6b7dd0d013ca946245ccf06ae2d957b21fd7675a2","last_reissued_at":"2026-05-18T04:05:57.919261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:57.919261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert modules associated to parabolically induced representations of semisimple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.OA","authors_text":"Pierre Clare","submitted_at":"2009-12-21T15:26:41Z","abstract_excerpt":"Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing modules. Considering G to be a semisimple Lie group and H to be the Levi component L of a parabolic subgroup P=LN, the Hilbert module associated to X=G/N encodes the P-series representations of G coming from parabolic subgroups associated to P. We provide several descriptions of this Hilbert module, corresponding to the classical pictures of P-series. We then chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4190","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":"0912.4190","created_at":"2026-05-18T04:05:57.919340+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.4190v2","created_at":"2026-05-18T04:05:57.919340+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4190","created_at":"2026-05-18T04:05:57.919340+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLKVQQ5GYPPP","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLKVQQ5GYPPPZDW3","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLKVQQ5G","created_at":"2026-05-18T12:26:02.257875+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/ZLKVQQ5GYPPPZDW3KX3LPXINAE","json":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE.json","graph_json":"https://pith.science/api/pith-number/ZLKVQQ5GYPPPZDW3KX3LPXINAE/graph.json","events_json":"https://pith.science/api/pith-number/ZLKVQQ5GYPPPZDW3KX3LPXINAE/events.json","paper":"https://pith.science/paper/ZLKVQQ5G"},"agent_actions":{"view_html":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE","download_json":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE.json","view_paper":"https://pith.science/paper/ZLKVQQ5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.4190&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLKVQQ5GYPPPZDW3KX3LPXINAE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLKVQQ5GYPPPZDW3KX3LPXINAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE/action/storage_attestation","attest_author":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE/action/author_attestation","sign_citation":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE/action/citation_signature","submit_replication":"https://pith.science/pith/ZLKVQQ5GYPPPZDW3KX3LPXINAE/action/replication_record"}},"created_at":"2026-05-18T04:05:57.919340+00:00","updated_at":"2026-05-18T04:05:57.919340+00:00"}