{"paper":{"title":"On a Class of Representations of Quantum Groups","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"A. Gerasimov, D. Lebedev, S. Kharchev, S. Oblezin","submitted_at":"2005-01-26T16:02:27Z","abstract_excerpt":"This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\\mathfrak{g})$, Yangian $Y(\\mathfrak{g})$ and affine quantum groups at zero level\n $U_q(\\hat{\\mathfrak{g}})_{c=0}$ corresponding to an arbitrary finite-dimensional semisimple Lie algebra $\\mathfrak{g}$. At the intermediate step we construct the embedding of the quantum groups into the algebra of the rational functions on the quantum multi-dimensional torus. The explicit parameterization of the quantum gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501473","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"}