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Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups

Alexander Givental·Yuan-Pin Lee
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Abstract

We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of the Langlands-dual quantized universal enveloping algebras U_q(g'). The conjecture is proved in the case of classical flag manifolds of the series A. The proof is based on a refinement of the famous Atiyah-Hirzebruch argument for rigidity of arithmetical genus applied to hyperquot-scheme compactifications of spaces of rational curves in the flag manifolds.

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Alexander Givental, Yuan-Pin Lee. 2001-08-15. Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups. https://arxiv.org/abs/math/0108105

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