Ultradifferentiable Chevalley theorems and isotropic functions

TL;DR

This paper establishes ultradifferentiable Chevalley restriction theorems for various classes, showing that isotropic functions' regularity is characterized by their restriction to diagonal matrices.

Contribution

It extends Chevalley restriction theorems to ultradifferentiable classes and characterizes the regularity of isotropic functions via their restrictions.

Findings

Ultradifferentiable Chevalley restriction theorems proven.

Isotropic functions' ultradifferentiable regularity characterized by restriction to diagonal matrices.

Applicable to a wide range of ultradifferentiable classes.

Abstract

We prove ultradifferentiable Chevelley restriction theorems for a wide range of ultradifferentiable classes. As a special case we find that isotropic functions, i.e., functions defined on the vector space of real symmetric matrices invariant under the action of the special orthogonal group by conjugation, possess some ultradifferentiable regularity if and only if their restriction to diagonal matrices has the same regularity.