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The Abelian/Nonabelian correspondence and Frobenius manifolds |
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| Authors: | Ionuţ Ciocan-Fontanine Bumsig Kim Claude Sabbah |
| Institution: | (1) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;(2) School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, 130-722 Seoul, Korea;(3) UMR 7640 du C.N.R.S., Centre de mathématiques Laurent Schwartz, école polytechnique, F-91128 Palaiseau cedex, France |
| Abstract: | We propose an approach via Frobenius manifolds to the study (began in BCK2] 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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