Reality and transversality for Schubert calculus in OG(n,2n+1)

TL;DR

This paper extends a key theorem in Schubert calculus to the orthogonal Grassmannian OG(n,2n+1), providing new insights into the geometric and combinatorial properties of this space.

Contribution

It proves an analogue of the Mukhin-Tarasov-Varchenko theorem for the maximal type B_n orthogonal Grassmannian OG(n,2n+1).

Findings

Established a new Schubert calculus result for OG(n,2n+1)

Extended the Shapiro-Shapiro conjecture to type B_n

Provided geometric insights into transversality in orthogonal Grassmannians

Abstract

We prove an analogue of the Mukhin-Tarasov-Varchenko theorem (formerly the Shapiro-Shapiro conjecture) for the maximal type B_n orthogonal Grassmannian OG(n,2n+1).