From groups to symmetric spaces

TL;DR

This paper investigates how properties and constructions known for reductive groups can be extended or adapted to symmetric spaces through theoretical analysis and experiments.

Contribution

It explores the generalization of reductive group properties to symmetric spaces, providing new insights and potential frameworks for further research.

Findings

Certain properties of reductive groups extend to symmetric spaces

Experimental results identify limitations of these generalizations

New conjectures or directions for symmetric space theory

Abstract

In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.