{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3776","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":""},"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"}