{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BPVX442OWFQ4S7XJJVYGRCYARB","short_pith_number":"pith:BPVX442O","schema_version":"1.0","canonical_sha256":"0beb7e734eb161c97ee94d70688b00885bd5c380ec57059e0cd5be37bb336f0b","source":{"kind":"arxiv","id":"1402.1717","version":2},"attestation_state":"computed","paper":{"title":"Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bent {\\O}rsted, Genkai Zhang, Jan M\\\"ollers","submitted_at":"2014-02-07T17:44:55Z","abstract_excerpt":"We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary series representations of $G$ and $G_1$ on Sobolev spaces on the nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$, respectively. The groups $N$ and $N_1$ are of H-type and we construct explicitly invariant differential operators between $N$ and $N_1$. These operators induce the projections onto the discrete components. Our construction "},"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":"1402.1717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-02-07T17:44:55Z","cross_cats_sorted":[],"title_canon_sha256":"ca1cef53e2b77f9677f2224ebcf9ed350c9f60ac931ab718ee5d1d917764ec65","abstract_canon_sha256":"9fdd053e25faaa48052cde6f6f453ef202ebcfdeca73c6e197eb5fa1318ceb96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:47.326765Z","signature_b64":"i8vu6pPENk5hKEe3vTtxBdBaXxLn5tfh5ADD75MPgq/U7yvmMGMYk/n5vycEAEExKn/uWMVZI04/H7gruPpzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0beb7e734eb161c97ee94d70688b00885bd5c380ec57059e0cd5be37bb336f0b","last_reissued_at":"2026-05-18T01:17:47.326071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:47.326071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bent {\\O}rsted, Genkai Zhang, Jan M\\\"ollers","submitted_at":"2014-02-07T17:44:55Z","abstract_excerpt":"We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary series representations of $G$ and $G_1$ on Sobolev spaces on the nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$, respectively. The groups $N$ and $N_1$ are of H-type and we construct explicitly invariant differential operators between $N$ and $N_1$. These operators induce the projections onto the discrete components. Our construction "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1717","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":"1402.1717","created_at":"2026-05-18T01:17:47.326177+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1717v2","created_at":"2026-05-18T01:17:47.326177+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1717","created_at":"2026-05-18T01:17:47.326177+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPVX442OWFQ4","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPVX442OWFQ4S7XJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPVX442O","created_at":"2026-05-18T12:28:22.404517+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/BPVX442OWFQ4S7XJJVYGRCYARB","json":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB.json","graph_json":"https://pith.science/api/pith-number/BPVX442OWFQ4S7XJJVYGRCYARB/graph.json","events_json":"https://pith.science/api/pith-number/BPVX442OWFQ4S7XJJVYGRCYARB/events.json","paper":"https://pith.science/paper/BPVX442O"},"agent_actions":{"view_html":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB","download_json":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB.json","view_paper":"https://pith.science/paper/BPVX442O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1717&json=true","fetch_graph":"https://pith.science/api/pith-number/BPVX442OWFQ4S7XJJVYGRCYARB/graph.json","fetch_events":"https://pith.science/api/pith-number/BPVX442OWFQ4S7XJJVYGRCYARB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB/action/storage_attestation","attest_author":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB/action/author_attestation","sign_citation":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB/action/citation_signature","submit_replication":"https://pith.science/pith/BPVX442OWFQ4S7XJJVYGRCYARB/action/replication_record"}},"created_at":"2026-05-18T01:17:47.326177+00:00","updated_at":"2026-05-18T01:17:47.326177+00:00"}