A mirror symmetric solution to the quantum Toda lattice
arXiv:0705.3202
Abstract
We use representation theory to construct integral formulas for solutions to the quantum Toda lattice in general type. This result generalizes work of Givental for SL(n)/B in a uniform way to arbitrary type and can be interpreted as a kind of mirror theorem for the full flag variety G/B. We also prove the existence of a totally positive critical point of the 'superpotential' in every mirror fiber.
25 pages, various improvements including to references, to appear in CMP