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Quantum cohomology of minuscule homogeneous spaces

Pierre-Emmanuel Chaput·Laurent Manivel·Nicolas Perrin
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Abstract

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality. In particular we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.

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Pierre-Emmanuel Chaput, Laurent Manivel, Nicolas Perrin. 2006-09-28. Quantum cohomology of minuscule homogeneous spaces. https://arxiv.org/abs/math/0607492

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