The Abelian/Nonabelian Correspondence and Frobenius Manifolds

Details The Abelian/Nonabelian Correspondence and Frobenius Manifolds The Abelian/Nonabelian Correspondence and Frobenius Manifolds

2006-10-09

arxiv.org/abs/math/0610265v1

Invent. Math. 171 (2008), no. 2, 301-343

Mathematics

Algebraic Geometry

35 pages, no figures

Scientific paper

10.1007/s00222-007-0082-x

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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