  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.
