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This representation is realized on the $L^2$-space of the minimal orbit $\\mathcal{O}$ of the structure group $L$ of $V$. We construct its corresponding $(\\mathfrak{g},\\mathfrak{k})$-module and show that it can be integrated to a unitary irreducible representation of $G$ on $L^2(\\mathcal{O})$.\n  In particular, we obtain a unified approach to the two most prominent minimal representations, namely the Segal--Shale--Weil representation of th","authors_text":"Jan M\\\"ollers","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-23T09:41:01Z","title":"Minimal representations of conformal groups and generalized Laguerre functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4549","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa9d861711fcc3b102e62b120118ef1177b7728d023a6086f9f2c2c369e37b9c","target":"record","created_at":"2026-05-18T03:47:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5e8ebc1176cee0e3e29221d800a9b818451fa029fd3c60d4467efc95a60535d9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-23T09:41:01Z","title_canon_sha256":"e173a2c7b5650b3d09451ccae3cb0f32ead79c735a2532fcc77baa8aecd49f32"},"schema_version":"1.0","source":{"id":"1009.4549","kind":"arxiv","version":3}},"canonical_sha256":"c0a55a3c9140de863b32ca30b73e0026faf8af5abb21cdd5f9fc52565fffe577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a55a3c9140de863b32ca30b73e0026faf8af5abb21cdd5f9fc52565fffe577","first_computed_at":"2026-05-18T03:47:08.995207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:08.995207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zNkyLJy1hqYnXBPgnCoK0H2WJgwBBm5e0PQG0VwBPEYzO4hmldtKAzUYNmWcsYae8LFvsd28Jf03Y0gCA23zBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:08.995842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4549","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa9d861711fcc3b102e62b120118ef1177b7728d023a6086f9f2c2c369e37b9c","sha256:9e386b22cb6af93e7ee0e2903cb6353b197495cc226c5c3c9a01378ddd9d802d"],"state_sha256":"b13d80d67618a7493fcaca8288673e6fabe9498cb2bfc05f7f50ff1edd5300ad"}