Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebras. III --Positive rational case--

TL;DR

This paper proves a Kazhdan-Lusztig type character formula for irreducible highest weight modules with positive rational weights over symmetrizable Kac-Moody Lie algebras, advancing understanding of their representation theory.

Contribution

It establishes the Kazhdan-Lusztig conjecture in the positive rational case for symmetrizable Kac-Moody Lie algebras, filling a key gap in the theory.

Findings

Proved the Kazhdan-Lusztig character formula for positive rational weights

Extended the conjecture to a broader class of Kac-Moody algebras

Enhanced understanding of representation theory for these algebras

Abstract

In this paper we prove the Kazhdan-Lusztig type character formula for irreducible highest weight modules with positive rational highest weights over symmetrizable Kac-Moody Lie algebras.