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Quantum cohomology for isotropic Grassmannians and Lefschetz exceptional collections Cruz Morales, John Alexander

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We will show by "generic smoothness" that the big quantum cohomology ring of isotropic Grassmannians \(IG(2,2n)\) is generically semisimple but the small quantum cohomology ring is not. That non-semisimplicity leads to a decomposition of the small quantum cohomology ring that relates to a certain decomposition of the derived category of \(IG(2,2n)\) in a so-called Lefschetz exceptional collection. This is based on joint work with A. Mellit, A. Kuznetsov, N. Perrin and M. Smirnov.

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