Quantum Cohomology of Minuscule Homogeneous Spaces III Semi-Simplicity and Consequences

By P. Chaput, Laurent Manivel, N. Perrin. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2007

57 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/937078a01fda86ae4cf8e76760641568553ccc28

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In Algebra and Number Theory

1. P. Chaput
2. N. Perrin

In Geometry and Topology

1. P. Chaput
2. N. Perrin
3. Anders Skovsted Buch
4. Leonardo Constantin Mihalcea

In Mathematical Physics

1. P. Chaput
2. N. Perrin

Citations in the corpus

• On the quantum cohomology of adjoint varieties (2009, background): “Recall that in the minuscule and cominuscule cases, it was proved in [8, 11] that the involution ι given by complex conjugation has the nice property of sending a Schubert class to a multiple of such a class.”