{"paper":{"title":"Standard Modules, Induction and the Temperley-Lieb Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"David Ridout, Yvan Saint-Aubin","submitted_at":"2012-04-20T00:00:13Z","abstract_excerpt":"The basic properties of the Temperley-Lieb algebra $TL_n$ with parameter $\\beta = q + q^{-1}$, for $q$ any non-zero complex number, are reviewed in a pedagogical way. The link and standard (cell) modules that appear in numerous physical applications are defined and a natural bilinear form on the standard modules is used to characterize their maximal submodules. When this bilinear form has a non-trivial radical, some of the standard modules are reducible and $TL_n$ is non-semisimple. This happens only when $q$ is a root of unity. Use of restriction and induction allows for a finer description o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4505","kind":"arxiv","version":4},"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"}