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Quantum cohomology of minuscule homogeneous spaces

Authors
  • Chaput, Pierre-Emmanuel
  • Manivel, Laurent
  • Perrin, Nicolas
Type
Published Article
Publication Date
Sep 28, 2006
Submission Date
Jul 20, 2006
Identifiers
arXiv ID: math/0607492
Source
arXiv
License
Unknown
External links

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

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