Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number

TL;DR

This paper proves the Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number, extending previous formulations and proofs to a broader class.

Contribution

The paper provides a proof of the Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number, generalizing earlier results.

Findings

Confirmed the Weyl denominator identity for a new class of affine Lie superalgebras

Extended the proof beyond the defect one case

Strengthened the theoretical understanding of affine Lie superalgebras

Abstract

Weyl denominator identity for the affinization of a basic Lie superalgebra with a non-zero Killing form was formulated by Kac and Wakimoto and was proven by them in defect one case. In this paper we prove this identity.