Characters of irreducible modules with non-critical highest weights over affine Lie algebras

TL;DR

This paper derives a Kazhdan-Lusztig type character formula for irreducible modules with non-critical highest weights over affine Lie algebras, expanding understanding of their structure using advanced functor techniques.

Contribution

It introduces a method to obtain character formulas for non-critical highest weight modules over affine Lie algebras from the rational case, employing translation, Enright, and Jantzen functors.

Findings

Derived Kazhdan-Lusztig type character formula for non-critical modules

Extended character formulas to arbitrary non-critical weights

Utilized functor techniques to connect rational and non-critical cases

Abstract

We shall derive Kazhdan-Lusztig type character formula for the irreducible modules with arbitrary non-critical highest weights over affine Lie algebras from the rational case by using the translation functor, the Enright functor and Jantzen's deformation argument.