The Cotangent Bundle of a Cominuscule Grassmannian

TL;DR

This paper generalizes a known embedding theorem for cotangent bundles of type A Grassmannians to all cominuscule generalized Grassmannians across different Lie types, revealing a broader geometric structure.

Contribution

It extends the embedding result of cotangent bundles into Schubert varieties from type A to all cominuscule generalized Grassmannians of arbitrary Lie type.

Findings

Cotangent bundles of all cominuscule Grassmannians can be embedded as open subsets of smooth Schubert varieties.

The embedding applies to generalized Grassmannians beyond type A, across various Lie types.

This unifies the geometric understanding of cotangent bundles in a broader class of homogeneous varieties.

Abstract

A theorem of the first author states that the cotangent bundle of the type $A$ Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety. We extend this result to cotangent bundles of cominuscule generalized Grassmannians of arbitrary Lie type.