Compact Simple Lie Groups and Their C-, S-, and E-Transforms

TL;DR

This paper introduces new continuous and discretized group transforms for compact simple Lie groups of rank two or higher, including the first-ever presentation of E-transforms, expanding the mathematical toolkit for analyzing these groups.

Contribution

It defines novel E-transforms for compact simple Lie groups of rank two or higher, extending existing C- and S-transforms and providing discretization methods for various lattice densities.

Findings

Introduces E-transforms for the first time.

Provides discretization methods for transforms over arbitrary lattice densities.

Extends mathematical framework for analyzing compact simple Lie groups.

Abstract

New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank $2\leq n<\infty$. Rank 1 transforms are known. Rank 2 exposition of $C$- and $S$-transforms is in the literature. The $E$-transforms appear here for the first time.