{"paper":{"title":"Quantum cohomology of the infinite dimensional generalized flag manifolds","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.DG","authors_text":"Augustin-Liviu Mare","submitted_at":"2001-05-16T16:31:00Z","abstract_excerpt":"Consider the infinite dimensional flag manifold $LK/T$ corresponding to the simple Lie group $K$ of rank $l$ and with maximal torus $T$. We show that, for $K$ of type $A$, $B$ or $C$, if we endow the space $H^*(LK/T)\\otimes \\bR[q_1,...,q_{l+1}]$ (where $q_1,...,q_{l+1}$ are multiplicative variables) with an $\\bR[\\{q_j\\}]$-bilinear product satisfying some simple properties analogous to the quantum product on $QH^*(K/T)$, then the isomorphism type of the resulting ring is determined by the integrals of motion of a certain periodic Toda lattice system, in exactly the same way as the isomorphism t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105133","kind":"arxiv","version":4},"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"}