The classification of thick representations of simple Lie groups

TL;DR

This paper characterizes and classifies thick representations of complex simple Lie groups, focusing on irreducible, weight multiplicity-free representations with totally ordered weight posets.

Contribution

It provides a complete classification of thick representations of connected complex simple Lie groups based on a new characterization involving weight multiplicity and order properties.

Findings

Thick representations are exactly the irreducible, weight multiplicity-free ones with totally ordered weight posets.

A full classification of thick representations for connected complex simple Lie groups is achieved.

The characterization simplifies understanding the structure of these representations.

Abstract

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets. Moreover, using this characterization, we give the classification of thick representations over ${\Bbb C}$ of connected complex simple Lie groups.