{"paper":{"title":"Elliptic quantum groups and their finite-dimensional representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.QA","authors_text":"Sachin Gautam, Valerio Toledano-Laredo","submitted_at":"2017-07-20T12:15:34Z","abstract_excerpt":"Let g be a complex semisimple Lie algebra, tau a point in the upper half-plane, and h a complex deformation parameter such that the image of h in the elliptic curve E_tau is of infinite order. In this paper, we give an intrinsic definition of the category of finite-dimensional representations of the elliptic quantum group E_{h,tau}(g) associated to g. The definition is given in terms of Drinfeld half-currents and extends that given by Enriquez-Felder for g=sl_2. When g=sl_n, it reproduces Felder's RLL definition via the Gauss decomposition obtained by Enriquez-Felder for n=2 and by the first a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06469","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"}