Quantum Hyperplane Section Theorem For Homogeneous Spaces

We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in homogeneous manifolds. For the proof we followed the scheme of Givental's proof of a mirror theorem for toric complete intersections.Comment: 24 pages, LaTeX 2e. The presentation is improved a lo

Quantum cohomology of flag manifolds G/B and quantum Toda lattices

We prove the Givental conjecture that the (equivariant) quantum cohomology of flag manifolds G/B are governed by the conservation law of Toda lattices. In addition, we find the quantum differential module structure of the flag manifolds.Comment: 19 pages, published versio