{"paper":{"title":"Generalizations of $Q$-systems and Orthogonal Polynomials from Representation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Darlayne Addabbo, Maarten Bergvelt","submitted_at":"2016-04-07T22:54:00Z","abstract_excerpt":"We briefly describe what tau-functions in integrable systems are. We then define a collection of tau-functions given as matrix elements for the action of $\\widehat{GL_2}$ on two-component Fermionic Fock space. These tau-functions are solutions to a discrete integrable system called a $Q$-system.\n  We can prove that our tau-functions satisfy $Q$-system relations by applying the famous \"Desnanot-Jacobi identity\" or by using \"connection matrices\", the latter of which gives rise to orthogonal polynomials. In this paper, we will provide the background information required for computing these tau-fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02190","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"}