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    Equivariant Giambelli Formulae for Grassmannians

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    Date
    2010
    Author
    Wilson, Elizabeth McLaughlin
    Advisor
    Tamvakis, Harry
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    Abstract
    In this thesis we use Young's raising operators to define and study polynomials which represent the Schubert classes in the equivariant cohomology ring of Grassmannians. For the type A and maximal isotropic Grassmannians, we show that our expressions coincide with the factorial Schur S, P, and Q functions. We define factorial theta polynomials, and conjecture that these represent the Schubert classes in the equivariant cohomology of non-maximal symplectic Grassmannians. We prove that the factorial theta polynomials satisfy the equivariant Chevalley formula, and that they agree with the type C double Schubert polynomials of [IMN] in some cases.
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    http://hdl.handle.net/1903/11190
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