Structure of parabolically induced modules for affine Kac-Moody algebras

TL;DR

This paper proves the irreducibility of a broad class of modules over affine Kac-Moody algebras induced from non-standard parabolic subalgebras, extending previous results and constructing new irreducible modules.

Contribution

It generalizes existing results on module irreducibility and introduces a new construction method for irreducible modules over affine Kac-Moody algebras.

Findings

Established irreducibility of modules for any non-standard parabolic subalgebra

Unified previous partial results into a comprehensive framework

Constructed many new irreducible modules

Abstract

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results and provides a a construction of many new irreducible modules.