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On Ideal Generators for Affine Schubert Varieties

V. Kreiman·V. Lakshmibai·P. Magyar·J. Weyman
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Abstract

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by restricting certain Plücker co-ordinates. As a consequence, we write an explicit set of generators for the degree-one part of the ideal of the finite-dimensional embedding. This in turn gives a set of generators for the degree-one part of the ideal defining the affine Grassmannian inside the infinite Grassmannian which we conjecture to be a complete set of ideal generators. We apply our results to the orbit closures of nilpotent matrices. We describe (in a characteristic-free way) a filtration for the coordinate ring of a nilpotent orbit closure and state a conjecture on the SL(n)-module structures of the constituents of this filtration.

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BibTeXRIS

V. Kreiman, V. Lakshmibai, P. Magyar, J. Weyman. 2004-11-06. On Ideal Generators for Affine Schubert Varieties. https://arxiv.org/abs/math/0411127

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