{"paper":{"title":"An affine deformation of the quantum cohomology ring of flag manifolds and periodic Toda lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.AG","authors_text":"Augustin-Liviu Mare, Leonardo C. Mihalcea","submitted_at":"2014-09-11T20:16:58Z","abstract_excerpt":"Consider the generalized flag manifold $G/B$ and the corresponding affine flag manifold $\\mathcal{Fl}_G$. In this paper we use curve neighborhoods for Schubert varieties in $\\mathcal{Fl}_G$ to construct certain affine Gromov-Witten invariants of $\\mathcal{Fl}_G$, and to obtain a family of \"affine quantum Chevalley\" operators $\\Lambda_0, \\ldots, \\Lambda_n$ indexed by the simple roots in the affine root system of $G$. These operators act on the cohomology ring $\\mathrm{H}^*(\\mathcal{Fl}_G)$ with coefficients in $\\mathbb{Z}[q_0, \\ldots,q_n]$. By analyzing commutativity and invariance properties o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3587","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"}