Mutations of puzzles and equivariant cohomology of two-step flag varieties

2014/01/14 by Buch, Anders Skovsted
#14M15 #14N35 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 05E05 #Secondary 14N15

paper · doi:10.48550/arxiv.1401.3065

Abstract

We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks to the equivariant version of the `quantum equals classical' result, our formula specializes to a Littlewood-Richardson rule for the equivariant quantum cohomology of Grassmannians.

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