The special linear representations of compact Lie groups

TL;DR

This paper explores a specific class of linear representations of compact Lie groups, called special linear representations, and discusses their properties and the extension of integral concepts within this framework.

Contribution

It introduces the concept of special linear representations of compact Lie groups and extends the notion of integration to these representations.

Findings

Defined the special linear representation for compact Lie groups

Extended the concept of integration to special linear representations

Provided foundational properties of these representations

Abstract

The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special linear representation for next using.