{"paper":{"title":"Spherical representations of Lie supergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Alexander Alldridge, Sebastian Schmittner","submitted_at":"2013-03-27T12:54:39Z","abstract_excerpt":"The classical Cartan-Helgason theorem characterises finite-dimensional spherical representations of reductive Lie groups in terms of their highest weights. We generalise the theorem to the case of a reductive symmetric supergroup pair $(G,K)$ of even type. Along the way, we compute the Harish-Chandra $c$-function of the symmetric superspace $G/K$. By way of an application, we show that all spherical representations are self-dual in type AIII|AIII."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6815","kind":"arxiv","version":2},"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"}