A mirror symmetric solution to the quantum Toda lattice
Konstanze Rietsch
TL;DR
This paper employs representation theory to develop integral formulas for solutions to the quantum Toda lattice across all types, extending previous work and establishing a mirror theorem for full flag varieties, along with positivity results.
Contribution
It introduces a uniform construction of integral solutions for the quantum Toda lattice in arbitrary type using representation theory, generalizing Givental's work.
Findings
Constructed integral formulas for quantum Toda solutions in general type.
Proved existence of a totally positive critical point of the superpotential.
Extended mirror symmetry results to full flag varieties.
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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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Algebra and Geometry