{"paper":{"title":"The idempotents of the TL_n-modules \\otimes^nC^2 in terms of elements of U_qsl_2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guillaume Provencher, Yvan Saint-Aubin","submitted_at":"2013-03-17T21:04:02Z","abstract_excerpt":"The vector space \\otimes^nC^2 upon which the XXZ Hamilonian with n spins acts bears the structure of a module over both the Temperley-Lieb algebra TL_n(\\beta=q+1/q) and the quantum algebra U_qsl_2. The decomposition of \\otimes^nC^2 as a U_qsl_2-module was first described by Rosso [23], Lusztig [15] and Pasquier and Saleur [20] and that as a TL_n-module by Martin [17] (see also Read and Saleur [21] and Gainutdinov and Vasseur [9]). For q generic, i.e. not a root of unity, the TL_n-module \\otimes^nC^2 is known to be a sum of irreducible modules. We construct the projectors (idempotents of the al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4102","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"}