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

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

2005-11-07

arxiv.org/abs/math/0511124v2

Mathematics

Algebraic Geometry

35 pages, revised version for publication in Adv. Math., in particular includes new section on the equivariant case in type A

Scientific paper

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.

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