General isotropic flags are general (for Grassmannian Schubert calculus)

TL;DR

This paper proves that for odd-orthogonal and symplectic groups, general isotropic flags ensure transversal intersections of Schubert cells on the Grassmannian, strengthening previous results in Schubert calculus.

Contribution

It establishes that general isotropic flags are sufficient for transversality in Schubert calculus on classical Grassmannians, extending prior work by Belkale and Kumar.

Findings

General isotropic flags guarantee transversal Schubert cell intersections.

Strengthens previous transversality results in Schubert calculus.

Applicable to odd-orthogonal and symplectic groups.

Abstract

We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert cells defined by such flags meet transversally. This strengthens a result of Belkale and Kumar in arXiv:0708.0398.