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    Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian

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    Date
    2017-04-04
    Author
    Shifler, Ryan M.
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    Abstract
    The odd symplectic Grassmannian IG := IG(k, 2n + 1) parametrizes k dimensional subspaces of C^2n+1 which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on IG with two orbits, and IG is itself a smooth Schubert variety in the submaximal isotropic Grassmannian IG(k, 2n + 2). We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of IG, i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case k = 2, and it gives an algorithm to calculate any quantum multiplication in the equivariant quantum cohomology ring.
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    http://hdl.handle.net/10919/77027
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    • Doctoral Dissertations [14204]

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