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Article Dans Une Revue Transformation Groups Année : 2008

Quantum cohomology of minuscule homogeneous spaces

Pierre-Emmanuel Chaput
Laurent Manivel
Nicolas Perrin
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Résumé

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 Poincar\'{e} duality. In particular we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.

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Dates et versions

hal-01256783 , version 1 (15-01-2016)

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Pierre-Emmanuel Chaput, Laurent Manivel, Nicolas Perrin. Quantum cohomology of minuscule homogeneous spaces. Transformation Groups, 2008, 13 (1), pp.47-89. ⟨10.1007/s00031-008-9001-5⟩. ⟨hal-01256783⟩
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