We prove the Weyl denominator identity for the affine Lie superalgebra gl(2|2)^ conjectured by V. Kac and M. Wakimoto. As it was pointed out in their paper, this gives another proof of Jacobi identity for the number of presentations of a given integer as a sum of eight squares.
A family of representations of the affine Lie superalgebra $\widehat{\mathfrak{gl}_{m|n}}(\mathbb{C})$
Simplicity of vacuum modules over affine Lie superalgebras
Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number
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