2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111483We explain how A. Givental's mirror symmetric family to the type A flag variety and its proposed generalization to partial flag varieties by Batyrev, Ciocan-Fontanine, Kim and van Straten relate to the Peterson variety Y in SL_n/B. We then use this theory to describe the totally nonnegative part of Y.Now published, corrected minor typo in the introduction. An early version appeared as ESI preprint 1674; 27 pages, 2 figuresAlgebraic Geometry20G20, 15A48, 14N35, 14N15text