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arXiv · 1401.3065

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

Anders Skovsted Buch
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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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Anders Skovsted Buch. 2014-01-14. Mutations of puzzles and equivariant cohomology of two-step flag varieties. https://arxiv.org/abs/1401.3065

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