{"paper":{"title":"Linear recurrence relations in $Q$-systems via lattice points in polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Chul-hee Lee","submitted_at":"2016-02-07T08:00:57Z","abstract_excerpt":"We prove that the sequence of the characters of the Kirillov-Reshetikhin (KR) modules $W_{m}^{(a)}, m\\in \\mathbb{Z}_{m\\geq 0}$ associated to a node $a$ of the Dynkin diagram of a complex simple Lie algebra $\\mathfrak{g}$ satisfies a linear recurrence relation except for some cases in types $E_7$ and $E_8$. To this end we use the $Q$-system and the existing lattice point summation formula for the decomposition of KR modules, known as domino removal rules when $\\mathfrak{g}$ is of classical type. As an application, we show how to reduce some unproven lattice point summation formulas in exception"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02347","kind":"arxiv","version":3},"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"}