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The Abelian/Nonabelian Correspondence and Frobenius Manifolds

Ionut Ciocan-Fontanine·Bumsig Kim·Claude Sabbah
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Abstract

We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ``abelianized'' quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.

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Ionut Ciocan-Fontanine, Bumsig Kim, Claude Sabbah. 2006-10-09. The Abelian/Nonabelian Correspondence and Frobenius Manifolds. https://doi.org/10.1007/s00222-007-0082-x

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