Equivariant Pieri Rules For Isotropic Grassmannians

TL;DR

This paper introduces a positive, manifestly clear Pieri rule for the torus-equivariant cohomology of isotropic Grassmannians in Lie types B, C, and D, extending known formulas and providing a new proof for type A.

Contribution

It presents the first positive, manifestly combinatorial Pieri rule for isotropic Grassmannians in types B, C, and D, and offers a simplified proof for the type A case.

Findings

First positive Pieri rule for types B, C, D Grassmannians

Simplified proof for the type A equivariant Pieri rule

Extension of Pieri rules to isotropic Grassmannians

Abstract

We give a Pieri rule for the torus-equivariant cohomology of (submaximal) Grassmannians of Lie types B, C, and D. To the authors' best knowledge, our rule is the first manifestly positive formula, beyond the equivariant Chevalley formula. We also give a simple proof of the equivariant Pieri rule for the ordinary (type A) Grassmannian.