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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} -
[ruan.tian:mathematical]
Y. Ruan and G. Tian, "A mathematical theory of quantum cohomology," Math. Res. Lett., vol. 1, iss. 2, pp. 269-278, 1994.
@article{ruan.tian:mathematical, mrkey = {1266766},
author = {Ruan, Yongbin and Tian, Gang},
title = {A mathematical theory of quantum cohomology},
journal = {Math. Res. Lett.},
fjournal = {Mathematical Research Letters},
volume = {1},
year = {1994},
number = {2},
pages = {269--278},
issn = {1073-2780},
mrclass = {58D15 (14N10 55N45 57R35 58F05)},
mrnumber = {1266766},
mrreviewer = {Bruce Hunt},
doi = {10.4310/MRL.1994.v1.n2.a15},
zblnumber = {0860.58006},
}