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arXiv · 1604.00053

On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian

Joel Kamnitzer·Dinakar Muthiah·Alex Weekes
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Abstract

We study spherical Schubert varieties in the affine Grassmannian. These Schubert varieties have a natural conjectural modular description due to Finkelberg-Mirkovi\'c. This modular description is easily seen to be set-theoretically correct, but it is not obviously scheme-theoretically correct. We prove that this modular description is correct in many cases. We also link this modular description to the reducedness conjecture from Kamnitzer-Webster-Weekes-Yacobi for tranverse slices in the affine Grassmannian.

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Joel Kamnitzer, Dinakar Muthiah, Alex Weekes. 2016-03-31. On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. https://arxiv.org/abs/1604.00053

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