{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A2TFS2IVGXCFFZ3LYQQJTFFQOB","short_pith_number":"pith:A2TFS2IV","schema_version":"1.0","canonical_sha256":"06a659691535c452e76bc4209994b0707e748add3dcdcb3d8f91041706aa9e79","source":{"kind":"arxiv","id":"2606.19783","version":1},"attestation_state":"computed","paper":{"title":"Convolution algebras associated to representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dragos Crisan","submitted_at":"2026-06-18T04:34:28Z","abstract_excerpt":"Given a complex reductive group $G$, a representation $V$ of $G$ and a Borel-stable subspace $M \\subset V$, we consider the associated Steinberg-type variety $Z$. We prove that, under a certain condition on $(V,M)$, called gluability, the equivariant Borel-Moore homology or $K$-theory of $Z$, equipped with the convolution product, is obtained as the intersection of two copies of the nil-Hecke algebra inside its localization. We also provide a description of these new algebras in terms of poles and residues. Similar results are obtained when $G$ is replaced by its loop group. This generalizes r"},"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":"2606.19783","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-18T04:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"c1b5a38e5a04f0c9eb84f2e4deec831b4fd36a4f1d1888e339fbed0c3f5c1a18","abstract_canon_sha256":"d4499e92d5514dcc03aa2d736be0eac1852913333412f1e21d77d8e5d8267332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:35.007566Z","signature_b64":"N9GVf0WM8T6UosNBaYSunAJrurGwCXYHFq2B+iv871b39MzGHLY8TdhfWSm3uVF+tzraDzhK0TqlxvlNgA1jDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06a659691535c452e76bc4209994b0707e748add3dcdcb3d8f91041706aa9e79","last_reissued_at":"2026-06-19T16:12:35.007208Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:35.007208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convolution algebras associated to representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dragos Crisan","submitted_at":"2026-06-18T04:34:28Z","abstract_excerpt":"Given a complex reductive group $G$, a representation $V$ of $G$ and a Borel-stable subspace $M \\subset V$, we consider the associated Steinberg-type variety $Z$. We prove that, under a certain condition on $(V,M)$, called gluability, the equivariant Borel-Moore homology or $K$-theory of $Z$, equipped with the convolution product, is obtained as the intersection of two copies of the nil-Hecke algebra inside its localization. We also provide a description of these new algebras in terms of poles and residues. Similar results are obtained when $G$ is replaced by its loop group. This generalizes r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19783","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19783/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.19783","created_at":"2026-06-19T16:12:35.007269+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19783v1","created_at":"2026-06-19T16:12:35.007269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19783","created_at":"2026-06-19T16:12:35.007269+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2TFS2IVGXCF","created_at":"2026-06-19T16:12:35.007269+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2TFS2IVGXCFFZ3L","created_at":"2026-06-19T16:12:35.007269+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2TFS2IV","created_at":"2026-06-19T16:12:35.007269+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/A2TFS2IVGXCFFZ3LYQQJTFFQOB","json":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB.json","graph_json":"https://pith.science/api/pith-number/A2TFS2IVGXCFFZ3LYQQJTFFQOB/graph.json","events_json":"https://pith.science/api/pith-number/A2TFS2IVGXCFFZ3LYQQJTFFQOB/events.json","paper":"https://pith.science/paper/A2TFS2IV"},"agent_actions":{"view_html":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB","download_json":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB.json","view_paper":"https://pith.science/paper/A2TFS2IV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19783&json=true","fetch_graph":"https://pith.science/api/pith-number/A2TFS2IVGXCFFZ3LYQQJTFFQOB/graph.json","fetch_events":"https://pith.science/api/pith-number/A2TFS2IVGXCFFZ3LYQQJTFFQOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB/action/storage_attestation","attest_author":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB/action/author_attestation","sign_citation":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB/action/citation_signature","submit_replication":"https://pith.science/pith/A2TFS2IVGXCFFZ3LYQQJTFFQOB/action/replication_record"}},"created_at":"2026-06-19T16:12:35.007269+00:00","updated_at":"2026-06-19T16:12:35.007269+00:00"}