Abstract
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].
Citation
Konstanze Rietsch. "A mirror construction for the totally nonnegative part of the Peterson variety." Nagoya Math. J. 183 105 - 142, 2006.
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