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A Mirror Symmetric Solution to the Quantum Toda Lattice |
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| Authors: | Konstanze?Rietsch author-information" > author-information__contact u-icon-before" > mailto:konstanze.rietsch@kcl.ac.uk" title=" konstanze.rietsch@kcl.ac.uk" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | 1.Department of Mathematics,King’s College London,London,UK |
| Abstract: | We give a representation-theoretic proof of a conjecture from Rietsch (Adv Math 217:2401–2442, 2008) providing 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 and totally negative critical point of the ‘superpotential’ in every mirror fiber. |
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