{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5BQNBFMX266G7EP737EB5YM7KJ","short_pith_number":"pith:5BQNBFMX","schema_version":"1.0","canonical_sha256":"e860d09597d7bc6f91ffdfc81ee19f524e1d4372d1520a50eed804c4088774ad","source":{"kind":"arxiv","id":"1708.04046","version":2},"attestation_state":"computed","paper":{"title":"On the Casselman-Jacquet functor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Yom Din, Dennis Gaitsgory, Tsao-Hsien Chen","submitted_at":"2017-08-14T09:31:26Z","abstract_excerpt":"We study the Casselman-Jacquet functor $J$, viewed as a functor from the (derived) category of $(\\mathfrak{g},K)$-modules to the (derived) category of $(\\mathfrak{g},N^-)$-modules, $N^-$ is the negative maximal unipotent. We give a functorial definition of $J$ as a certain right adjoint functor, and identify it as a composition of two averaging functors $\\text{Av}^{N^-}_!\\circ \\text{Av}^N_*$. We show that it is also isomorphic to the composition $\\text{Av}^{N^-}_*\\circ \\text{Av}^N_!$. Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) $D$-modules on an"},"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":"1708.04046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-14T09:31:26Z","cross_cats_sorted":[],"title_canon_sha256":"7b311ab169ac7d5cd6c4d293335d3eb37473bf9e5ad9882068017b1ce1746b1f","abstract_canon_sha256":"45d0cb78c13b1d9a7e9719962d2b15aec66b34c328a2dce455d82bf5ad0a6109"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:03.303124Z","signature_b64":"RU8Xe9STO3Z0hk3z+PJpDkaPnTOi5IcCAVwjeeQPZetobX2F59I1WYP2wI0gzkljVJL2r+nBFvyvw6A70KRUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e860d09597d7bc6f91ffdfc81ee19f524e1d4372d1520a50eed804c4088774ad","last_reissued_at":"2026-05-17T23:57:03.302490Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:03.302490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Casselman-Jacquet functor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Yom Din, Dennis Gaitsgory, Tsao-Hsien Chen","submitted_at":"2017-08-14T09:31:26Z","abstract_excerpt":"We study the Casselman-Jacquet functor $J$, viewed as a functor from the (derived) category of $(\\mathfrak{g},K)$-modules to the (derived) category of $(\\mathfrak{g},N^-)$-modules, $N^-$ is the negative maximal unipotent. We give a functorial definition of $J$ as a certain right adjoint functor, and identify it as a composition of two averaging functors $\\text{Av}^{N^-}_!\\circ \\text{Av}^N_*$. We show that it is also isomorphic to the composition $\\text{Av}^{N^-}_*\\circ \\text{Av}^N_!$. Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) $D$-modules on an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04046","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":"1708.04046","created_at":"2026-05-17T23:57:03.302587+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04046v2","created_at":"2026-05-17T23:57:03.302587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04046","created_at":"2026-05-17T23:57:03.302587+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BQNBFMX266G","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BQNBFMX266G7EP7","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BQNBFMX","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.23167","citing_title":"What is the Geometric Langlands Correspondence about?","ref_index":165,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ","json":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ.json","graph_json":"https://pith.science/api/pith-number/5BQNBFMX266G7EP737EB5YM7KJ/graph.json","events_json":"https://pith.science/api/pith-number/5BQNBFMX266G7EP737EB5YM7KJ/events.json","paper":"https://pith.science/paper/5BQNBFMX"},"agent_actions":{"view_html":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ","download_json":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ.json","view_paper":"https://pith.science/paper/5BQNBFMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04046&json=true","fetch_graph":"https://pith.science/api/pith-number/5BQNBFMX266G7EP737EB5YM7KJ/graph.json","fetch_events":"https://pith.science/api/pith-number/5BQNBFMX266G7EP737EB5YM7KJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ/action/storage_attestation","attest_author":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ/action/author_attestation","sign_citation":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ/action/citation_signature","submit_replication":"https://pith.science/pith/5BQNBFMX266G7EP737EB5YM7KJ/action/replication_record"}},"created_at":"2026-05-17T23:57:03.302587+00:00","updated_at":"2026-05-17T23:57:03.302587+00:00"}