{"paper":{"title":"The centralizer of $K$ in $U(\\mathfrak{g}) \\otimes C(\\mathfrak{p})$ for the group $SO_e(4,1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ana Prli\\'c","submitted_at":"2017-04-25T21:01:31Z","abstract_excerpt":"Let $G$ be the Lie group $SO_e(4,1)$, with maximal compact subgroup $K = S(O(4) \\times O(1))_e\\cong SO(4)$. Let $\\mathfrak{g}=\\mathfrak{so}(5,\\mathbb{C})$ be the complexification of the Lie algebra $\\mathfrak{g}_0 = \\mathfrak{so}(4,1)$ of $G$, and let $U(\\mathfrak{g})$ be the universal enveloping algebra of $\\mathfrak{g}$. Let $\\mathfrak{g} = \\mathfrak{k} \\oplus \\mathfrak{p}$ be the Cartan decomposition of $\\mathfrak{g}$, and $C(\\mathfrak{p})$ the Clifford algebra of $\\mathfrak{p}$ with respect to the trace form $B(X, Y) = \\text{tr}(XY)$ on $\\mathfrak{p}$. In this paper we give explicit genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07903","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"}