{"paper":{"title":"Olshanski spherical functions for infinite dimensional motion groups of fixed rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CA","authors_text":"Margit R\\\"osler, Michael Voit","submitted_at":"2012-10-04T09:33:55Z","abstract_excerpt":"Consider the Gelfand pairs $(G_p,K_p):=(M_{p,q} \\rtimes U_p,U_p)$ associated with motion groups over the fields $\\mathbb F=\\mathbb R,\\mathbb C,\\mathbb H$ with $p\\geq q$ and fixed $q$ as well as the inductive limit $p\\to\\infty$,the Olshanski spherical pair $(G_\\infty,K_\\infty)$. We classify all Olshanski spherical functions of $(G_\\infty,K_\\infty)$ as functions on the cone $\\Pi_q$ of positive semidefinite $q\\times q$-matrices and show that they appear as (locally) uniform limits of spherical functions of $(G_p,K_p)$ as $p\\to\\infty$. The latter are given by Bessel functions on $\\Pi_q$. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1351","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"}