A mirror symmetric construction of qH*_T(G/P)_(q)

Abstract

Let 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 A

Cited by in corpus (5)

• A Landau-Ginzburg model for Lagrangian Grassmannians, Langlands duality and relations in quantum cohomology
• More Toda-like (0,2) mirrors
• Geometry of canonical bases and mirror symmetry
• Bridge graphs and Deodhar parametrizations for positroid varieties
• Cyclic stratum of Frobenius manifolds, Borel-Laplace $(\mathbf{\alpha },\mathbf{\beta })$-multitransforms, and integral representations of solutions of Quantum Differential Equations