Nagoya Mathematical Journal

A mirror construction for the totally nonnegative part of the Peterson variety

Konstanze Rietsch

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We explain how A. Givental's mirror symmetric family [14] to the type $A$ flag variety and its proposed generalization [3] to partial flag varieties by Batyrev, Ciocan-Fontanine, Kim and van Straten relate to the Peterson variety $Y \subset SL_{n}/B$. We then use this theory to describe the totally nonnegative part of $Y$, extending a result from [30].

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Nagoya Math. J., Volume 183 (2006), 105-142.

First available in Project Euclid: 5 September 2006

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Primary: 20G20: Linear algebraic groups over the reals, the complexes, the quaternions 15A48 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 14N15: Classical problems, Schubert calculus

flag varieties quantum cohomology mirror symmetry total positivity


Rietsch, Konstanze. A mirror construction for the totally nonnegative part of the Peterson variety. Nagoya Math. J. 183 (2006), 105--142.

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