Mutations of Puzzles and Equivariant Cohomology of Two-step Flag Varieties
نویسنده
چکیده
We introduce a mutation algorithm for puzzles that is a threedirection 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.
منابع مشابه
Schubert Calculus and Puzzles
1. Interval positroid varieties 1 1.1. Schubert varieties 1 1.2. Schubert calculus 2 1.3. First positivity result 3 1.4. Interval rank varieties 5 2. Vakil’s Littlewood-Richardson rule 7 2.1. Combinatorial shifting 7 2.2. Geometric shifting 7 2.3. Vakil’s degeneration order 9 2.4. Partial puzzles 10 3. Equivariant and Kextensions 11 3.1. K-homology 11 3.2. K-cohomology 12 3.3. Equivariant K-the...
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