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

2005/11/07 by Rietsch, Konstanze · 4 citations
#15A48 #20G20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0511124

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.

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