2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136468Let G be a simple simply connected complex algebraic group. We give a Lie theoretic construction of a conjectural mirror family associated to a general flag variety G/P, and show that it recovers the Peterson variety presentation for the T-equivariant quantum cohomology rings qH*_T(G/P)_(q) with quantum parameters inverted. For SL_n/B we relate our construction to the mirror family defined by Givental and its T-equivariant analogue due to Joe and Kim.35 pages, revised version for publication in Adv. Math., in particular includes new section on the equivariant case in type AAlgebraic Geometry20G20, 15A48text