Cuspidal representations of sl(n+1)

TL;DR

This paper classifies and explicitly describes all indecomposable cuspidal modules within the category of weight modules over the Lie algebra sl(n+1), advancing understanding of their structure.

Contribution

It provides a complete classification and explicit description of indecomposable cuspidal modules for sl(n+1), a significant step in representation theory.

Findings

Complete classification of indecomposable cuspidal modules

Explicit descriptions provided for each module

Advances understanding of weight module structures

Abstract

In this paper we study the subcategory of cuspidal modules of the category of weight modules over the Lie algebra sl(n+1). Our main result is a complete classification and explicit description of the indecomposable cuspidal modules.