Topological-antitopological fusion and the quantum cohomology of Grassmannians

@article{Guest2021TopologicalantitopologicalFA,
  title={Topological-antitopological fusion and the quantum cohomology of Grassmannians},
  author={Martin A. Guest},
  journal={Japanese Journal of Mathematics},
  year={2021},
  volume={16},
  pages={155-183}
}
  • M. Guest
  • Published 2 December 2020
  • Physics, Mathematics
  • Japanese Journal of Mathematics
We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as their respective Stokes data, based on the original physics approach using the tt* equations. We also use the Stokes data of the tt* equations to provide a Lie-theoretic link between particles in affine Toda models and solitons in certain sigma-models. Along the way, we review some old ideas from… 
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We review some links between Lie-theoretic polytopes and field theories in physics, which were proposed in the 1990’s. A basic ingredient is the Coxeter Plane, whose relation to integrable systems
Positive energy representations of affine algebras and Stokes matrices of the affine Toda equations
We give a construction which produces a positive energy representation of the affine Lie algebra ŝln+1C from the Stokes data of a solution of the tt*-Toda equations. The construction appears to play
Symplectic aspects of the tt*-Toda equations
  • Ryosuke Odoi
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
We evaluate explicitly, in terms of the asymptotic data, the ratio of the constant pre-factors in the large and small x asymptotics of the tau functions for global solutions of the tt*-Toda

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