{"paper":{"title":"Difference Hierarchies for $nT$ $\\tau$-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Darlayne Addabbo, Maarten Bergvelt","submitted_at":"2016-11-30T20:20:51Z","abstract_excerpt":"We introduce hierarchies of difference equations (referred to as $nT$-systems) associated to the action of a (centrally extended, completed) infinite matrix group $GL_{\\infty}^{(n)}$ on $n$-component fermionic Fock space. The solutions are given by matrix elements ($\\tau$-functions) for this action. We show that the $\\tau$-functions of type $nT$ satisfy bilinear equations of length $3,4,\\dots,n+1$. The $2T$-system is, after a change of variables, the usual $3$ term $T$-system of type $A$.\n  Restriction from $GL_{\\infty}^{(n)}$ to a subgroup isomorphic to the loop group $LGL_{n}$, defines $nQ$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10340","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"}