Abstract view
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Quantum Cohomology of Minuscule Homogeneous Spaces III. Semi-Simplicity and Consequences
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Published:2010-06-18
Printed: Dec 2010
P. E. Chaput,
Laboratoire de Mathématiques Jean Leray, UFR Sciences et Techniques, Nantes, France
L. Manivel,
Institut Fourier, Université de Grenoble I, Saint-Martin d'Héres, France
N. Perrin,
Institut de Mathématiques, Université Pierre et Marie Curie, PARIS, France
Abstract
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.
| MSC Classifications: |
14M15, 14N35 show english descriptions
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
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]
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