The Abelian/Nonabelian Correspondence and Frobenius Manifolds

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.

35 pages, no figures

References in corpus (3)

• Geometry and analytic theory of Frobenius manifolds
• Symplectic quotients by a nonabelian group and by its maximal torus
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture

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