Quantum Cohomology of Minuscule Homogeneous Spaces III. Semi-Simplicity and Consequences
Printed: Dec 2010
P. E. Chaput,
We prove that the quantum cohomology ring of any minuscule or
cominuscule homogeneous space, specialized at $q=1$, is semisimple.
This implies that complex conjugation defines an algebra automorphism
of the quantum cohomology ring localized at the quantum
parameter. We check that this involution coincides with the strange
duality defined in our previous article. We deduce Vafa--Intriligator type
formulas for the Gromov--Witten invariants.
quantum cohomology, minuscule homogeneous spaces, Schubert calculus, quantum Euler class
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]