Reducedness of affine Grassmannian slices in type A
Joel Kamnitzer, Dinakar Muthiah, Alex Weekes, Oded Yacobi
TL;DR
This paper proves a conjecture in type A that characterizes the ideals of transversal slices to spherical Schubert varieties in the affine Grassmannian, providing a modular description of these varieties.
Contribution
It establishes the ideal description of affine Grassmannian slices in type A and confirms a conjecture, enhancing understanding of their geometric structure.
Findings
Confirmed the conjecture for type A affine Grassmannian slices.
Provided a modular description of spherical Schubert varieties.
Described the ideal of transversal slices explicitly.
Abstract
We prove in type A a conjecture which describes the ideal of transversal slices to spherical Schubert varieties in the affine Grassmannian. As a corollary, we prove a modular description (due to Finkelberg-Mirkovi\'c) of the spherical Schubert varieties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.