Asian Journal of Mathematics

Volume 19 (2015)

Number 2

Functorial relationships between $QH* (G/B)$ and $QH* (G/P)$, II

Pages: 203 – 234



Changzheng Li (Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, The University of Tokyo, Kashiwa City, Chiba, Japan)


We show a canonical injective morphism from the quantum cohomology ring $QH* (G/P)$ to the associated graded algebra of $QH* (G/B)$, which is with respect to a nice filtration on $QH* (G/B)$ introduced by Leung and the author. This tells us the vanishing of a lot of genus zero, three-pointed Gromov-Witten invariants of flag varieties $G/P$.


quantum cohomology, flag varieties, filtered algebras, Gromov-Witten invariants

2010 Mathematics Subject Classification

14M15, 14N35

Published 25 March 2015