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

• 成果类型: Article
• 署名作者: Buch, Anders Skovsted
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.182.1.4
• 发表日期: 2015
• 页码: 173-220
• 关键词: littlewood-richardson rule; quantum cohomology; homogeneous spaces; Positivity; ring

摘要

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 Grassmanniaus.