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

Pages 173-220 from Volume 182 (2015), Issue 1 by Anders Skovsted Buch

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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Keywords
, , , , , , ,
Mathematical Subject Classification
Primary: Secondary: , ,
DOI
https://doi.org/10.4007/annals.2015.182.1.4
MR
3374959
zbMATH
06456008
Milestones
Received: 28 October 2013
Revised: 27 August 2014
Accepted: 28 August 2014

Authors

Anders Skovsted Buch

Rutgers University, Piscataway, NJ