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The associated orbit spaces may be identified with $\\Pi_q\\times \\b R$ and $\\Xi_q\\times \\b R$ respectively with the cone $\\Pi_q$ of positive semidefinite matrices and the Weyl chamber $\\Xi_q={x\\in\\b R^q: x_1\\ge...\\ge x_q\\ge 0}$.\n  In this paper we compute the associated convolutions on $\\Pi_q\\times \\b R$ and $\\Xi_q\\times \\b R$ expli"},"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":"1201.3776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-18T13:02:32Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e50ffc17f9cba30be425cd113c2f1ab4ede829e7d8e1a00356ca14ca3fd96bab","abstract_canon_sha256":"7d95345802984b6aabf615b19cdbd332e900f2461d3c54c66421635dd771acbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:18.055804Z","signature_b64":"4TtbhKkA8BKYhqdnhURUKscV5MjkEmEMh8ouu7a5j6n/CiHdE9iYTcte57VvcrdMKGpFsKDBDKTyguw63czYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"796495ee53f5485a15a22d19cea093c2b768e5a9cbe6669374550bf3fa6922fb","last_reissued_at":"2026-05-18T04:04:18.054993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:18.054993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CA","authors_text":"Michael Voit","submitted_at":"2012-01-18T13:02:32Z","abstract_excerpt":"Let $p,q$ positive integers. The groups $U_p(\\b C)$ and $U_p(\\b C)\\times U_q(\\b C) $ act on the Heisenberg group $H_{p,q}:=M_{p,q}(\\b C)\\times \\b R$ canonically as groups of automorphisms where $M_{p,q}(\\b C)$ is the vector space of all complex $p\\times q$-matrices. 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