Generalized Imaginary Verma and Wakimoto modules

TL;DR

This paper introduces a unified method for constructing new irreducible modules for affine Kac-Moody algebras using parabolic induction, generalizing previous results and providing explicit realizations through generalized Imaginary Wakimoto modules.

Contribution

It develops a general technique for constructing irreducible modules for affine Kac-Moody algebras, extending and unifying prior approaches with explicit realizations.

Findings

New irreducible weight modules constructed for affine Kac-Moody algebras.

Generalized Imaginary Wakimoto modules provide explicit realizations.

Method applies to cases with infinite-dimensional Levi factors and nonzero central charge.

Abstract

We develop a general technique of constructing new irreducible weight modules for any affine Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic subalgebra is infinite-dimensional and the central charge is nonzero. Our approach uniforms and generalizes all previously known results with imposed restrictions on inducing modules. We also define generalized Imaginary Wakimoto modules which provide an explicit realization for generic generalized Imaginary Verma modules.