Curve neighborhoods of Schubert Varieties in the odd symplectic Grassmannian

Clelia Pech; Ryan M. Shifler

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arXiv · 2011.05221

Curve neighborhoods of Schubert Varieties in the odd symplectic Grassmannian

Clelia Pech·Ryan M. Shifler

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Abstract

Let $\mbox{IG}(k,2n+1)$ be the odd symplectic Grassmannian. It is a quasi-ho\-mo\-ge\-neous space with homogeneous-like behavior. A very limited description of curve neighborhoods of Schubert varieties in $\mbox{IG}(k,2n+1)$ was used by Mihalcea and the second named author to prove an (equivariant) quantum Chevalley rule. In this paper we give a full description of the irreducible components of curve neighborhoods in terms of the Hecke product of (appropriate) Weyl group elements, $k$-strict partitions, and BC-partitions. The latter set of partitions respect the Bruhat order with inclusions. Our approach follows the philosophy of Buch and Mihalcea's curve neighborhood calculations of Schubert varieties in the homogeneous cases.

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Clelia Pech, Ryan M. Shifler. 2020-11-10. Curve neighborhoods of Schubert Varieties in the odd symplectic Grassmannian. https://arxiv.org/abs/2011.05221

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