An affine approach to Peterson comparison
Combinatorics
2021-06-17 v2 Algebraic Geometry
Abstract
The Peterson comparison formula proved by Woodward relates the three-pointed Gromov-Witten invariants for the quantum cohomology of partial flag varieties to those for the complete flag. Another such comparison can be obtained by composing a combinatorial version of the Peterson isomorphism with a result of Lapointe and Morse relating quantum Littlewood-Richardson coefficients for the Grassmannian to k-Schur analogs in the homology of the affine Grassmannian obtained by adding rim hooks. We show that these comparisons on quantum cohomology are equivalent, up to Postnikov's strange duality isomorphism.
Cite
@article{arxiv.2008.13765,
title = {An affine approach to Peterson comparison},
author = {Linda Chen and Elizabeth Milićević and Jennifer Morse},
journal= {arXiv preprint arXiv:2008.13765},
year = {2021}
}
Comments
28 pages; added several references, final version to appear in Algebr. Represent. Theory