Kreiman-Lakshmibai-Magyar-Weyman Ideas

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I'll discuss an ongoing project of mine with Dinakar Muthiah and Oded Yacobi, which is based on ideas of Kreiman-Lakshmibai-Magyar-Weyman.  It is aimed at developing a "nice" standard monomial theory for the affine Grassmannian in type A, where "nice" means hopefully close in spirit to Hodge's classical standard monomial theory for finite dimensional Grassmannians.