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

This article discusses Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups. The results of the paper were completed in the Summer 98 and reported by the authors at a number of conferences and seminars. In this version of the paper researchers decided to leave the material of Section 5 in the form close to the preliminary text written in 1998. In particular, researchers did not try to match the quantum group description of finite-difference Toda lattices given in Section 5 with the construction that has become standard since then due to the paper by writer P. Etingof.