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

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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.

Original languageEnglish (US)
Pages (from-to)173-220
Number of pages48
JournalAnnals of Mathematics
Volume182
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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