A mirror symmetric solution to the quantum Toda lattice

Details A mirror symmetric solution to the quantum Toda lattice A mirror symmetric solution to the quantum Toda lattice

2007-05-22

arxiv.org/abs/0705.3202v3

Mathematics

Representation Theory

25 pages, various improvements including to references, to appear in CMP

Scientific paper

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.

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