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.

Woodward 证明的 Peterson 比较公式将部分标志变体的量子上同调的三点 Gromov-Witten 不变量与完整标志的三点 Gromov-Witten 不变量联系起来。另一个这样的比较可以通过组合 Peterson 同构的组合版本来获得，其中 Lapointe 和 Morse 将 Grassmannian 的量子 Littlewood-Richardson 系数与通过添加 rim hook 获得的仿射 Grassmannian 的同源性中的k- Schur 类似物相关联。我们证明了这些关于量子上同调的比较是等价的，直到 Postnikov 奇怪的对偶同构。