Universal equations for maximal isotropic Grassmannians

TL;DR

This paper demonstrates that all maximal isotropic Grassmannians can be described by pulling back equations from specific low-dimensional cases, simplifying their algebraic characterization.

Contribution

It establishes a universal method to define maximal isotropic Grassmannians via pullbacks from known smaller cases, unifying their algebraic descriptions.

Findings

Maximal isotropic Grassmannians can be characterized by pullbacks from $Gr_{iso}(3,7)$ or $Gr_{iso}(4,8)$.

A universal algebraic description for these Grassmannians is provided.

The approach simplifies understanding the equations defining isotropic Grassmannians.

Abstract

The isotropic Grassmannian parametrizes isotropic subspaces of a vector space equipped with a quadratic form. In this paper, we show that any maximal isotropic Grassmannian in its Pl\"ucker embedding can be defined by pulling back the equations of $Gr_{\operatorname{iso}}(3,7)$ or $Gr_{\operatorname{iso}}(4,8)$.