A mirror symmetric solution to the quantum Toda lattice

Konstanze Rietsch

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arXiv · 0705.3202

A mirror symmetric solution to the quantum Toda lattice

Konstanze Rietsch

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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.

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Konstanze Rietsch. 2011-03-26. A mirror symmetric solution to the quantum Toda lattice. https://arxiv.org/abs/0705.3202

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