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Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation of Mp(N,R) and the minimal unitary representation of O(N+1,2) keeping smaller symmetries.\n  We prove that this action \\omega_{k,a} lifts to a unitary representation of the universal covering of SL(2,R), and can even be extended to a holomorphic semigroup \\Omega_{k,a}. In the k\\equiv 0 case, our semigroup generalizes the Hermite"},"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":"0907.3749","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-22T06:10:08Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.QA"],"title_canon_sha256":"e97eafd7b90c4f61bb9b4ca545a4db4137fb9cb6b7456d6775d3704593a4f9db","abstract_canon_sha256":"7aaec8544de261792666ffcb0482d6445b31a75d03840c628da37b22871def2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.989773Z","signature_b64":"d/iKw2n3I6rDXqgaJxWDTK0g3UwfweXrkkGSDj1RYSbOJytH85ANdkc20u1bMwHJoFS3kEwgXCbF2TcIujf9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d395dcd7377c43876824757156829ae853986a3ac277840dfbd03e60cbd7b18","last_reissued_at":"2026-05-17T23:53:19.989266Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.989266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laguerre semigroup and Dunkl operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Bent Orsted, Salem Ben Said, Toshiyuki Kobayashi","submitted_at":"2009-07-22T06:10:08Z","abstract_excerpt":"We construct a two-parameter family of actions \\omega_{k,a} of the Lie algebra sl(2,R) by differential-difference operators on R^N \\setminus {0}. 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