Minimal dimension equivariant embeddings of real and complex flag manifolds into Euclidean spaces

TL;DR

This paper determines the smallest Euclidean space dimension into which real and complex flag manifolds can be equivariantly embedded under orthogonal and unitary group actions, respectively.

Contribution

It identifies the minimal equivariant embedding dimension for real and complex flag manifolds, achieved via isospectral models, advancing understanding of their geometric representations.

Findings

Minimal embedding dimension for real flag manifolds under orthogonal groups.

Minimal embedding dimension for complex flag manifolds under unitary groups.

Achieved minimal embeddings using isospectral models.

Abstract

We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.