Some conjectures regarding certain Schubert structure constants in Lie types B and D

TL;DR

This paper presents conjectures about Schubert structure constants in Lie types B and D, focusing on specific Richardson varieties and their stability under certain Levi subgroups, advancing understanding in Schubert calculus.

Contribution

It introduces new conjectural rules for calculating Schubert structure constants in Lie types B and D for particular Richardson varieties.

Findings

Proposes conjectural formulas for Schubert structure constants.

Identifies stability conditions of Richardson varieties under Levi subgroups.

Provides detailed conjectures to guide future proofs and computations.

Abstract

I give the details of some conjectures regarding Schubert calculus in Lie types B and D. Specifically, I conjecture rules for Schubert structure constants $c_{u,v}^w$ when $X_{w_0u}^v$ is a Richardson variety stable under the spherical Levi subgroup $\C^* \times SO(n-2,\C)$ of $SO(n,\C)$.