{"paper":{"title":"The Rahman polynomials and the Lie algebra sl_3(C)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.RT","authors_text":"Paul Terwilliger, Plamen Iliev","submitted_at":"2010-06-25T20:33:32Z","abstract_excerpt":"We interpret the Rahman polynomials in terms of the Lie algebra $sl_3(C)$. Using the parameters of the polynomials we define two Cartan subalgebras for $sl_3(C)$, denoted $H$ and $\\tilde{H}$. We display an antiautomorphism $\\dagger$ of $sl_3(C)$ that fixes each element of $H$ and each element of $\\tilde{H}$. We consider a certain finite-dimensional irreducible $sl_3(C)$-module $V$ consisting of homogeneous polynomials in three variables. We display a nondegenerate symmetric bilinear form $<,>$ on $V$ such that $<\\beta \\xi,\\zeta> = < \\xi,\\beta^\\dagger \\zeta>$ for all $\\beta \\in sl_3(C)$ and $\\x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5062","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"}