Singular Riemannian foliations and their quadratic basic polynomials

TL;DR

This paper establishes a novel connection between the invariant theory of singular Riemannian foliations and Jordan algebras, leading to new structural insights and characterizations of Clifford foliations.

Contribution

It introduces a new link between invariant theory and Jordan algebras, and characterizes Clifford foliations via basic polynomials, advancing the understanding of infinitesimal foliations.

Findings

Link between invariant theory and Jordan algebras

Characterization of Clifford foliations using basic polynomials

Existence of non-trivial symmetries in infinitesimal foliations

Abstract

We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the recently discovered Clifford foliations in terms of basic polynomials. This link also yields new structural results about infinitesimal foliations, such as the existence of non-trivial symmetries.