{"paper":{"title":"Evaluation modules for the $q$-tetrahedron algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Hjalmar Rosengren, Paul Terwilliger, Tatsuro Ito","submitted_at":"2013-08-15T19:17:30Z","abstract_excerpt":"Let $\\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \\in \\mathbb F$ that is not a root of unity. We consider the $q$-tetrahedron algebra $\\boxtimes_q$ over $\\mathbb F$. It is known that each finite-dimensional irreducible $\\boxtimes_q$-module of type 1 is a tensor product of evaluation modules. This paper contains a comprehensive description of the evaluation modules for $\\boxtimes_q$. This description includes the following topics. Given an evaluation module $V$ for $\\boxtimes_q$, we display 24 bases for $V$ that we find attractive. For each basis we give the matrices th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3480","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"}