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

Abstract

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.

19 pages, published version

References in corpus (2)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Higher genus symplectic invariants and sigma model coupled with gravity

Cited by in corpus (3)

• Defects and Quantum Seiberg-Witten Geometry
• A Landau-Ginzburg model for Lagrangian Grassmannians, Langlands duality and relations in quantum cohomology
• Lecture notes on quantum cohomology of the flag manifold