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

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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.
25 pages

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Algebraic Geometry, Representation Theory, 14N35

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http://salesiana.dossiersoluciones.com/handle/123456789/62022

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108105
 http://arxiv.org/abs/math/0108105

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arXiv