The discriminants associated to isotropy representations of symmetric spaces

TL;DR

This paper introduces a generalized discriminant linked to symmetric spaces, extending the concept from real symmetric matrices, and explores its representation as a sum of squares with methods to estimate the minimal number of squares needed.

Contribution

It develops a new method to estimate the minimal sum of squares representation for discriminants of symmetric spaces, generalizing classical results.

Findings

Discriminant can be expressed as a sum of squares of real polynomials.

A method to estimate the minimal number of squares is proposed.

Applications to specific examples demonstrate the approach.

Abstract

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.