An extension of Macdonald's identity for ${\mathfrak{sl}}_n$

Abstract

Let $n$ be an odd positive integer. In this short elementary note, we slightly extend Macdonald's identity for ${\mathfrak{sl}}_n$ into a two-variables identity in the spirit of Jacobi forms. The peculiarity of this work lies in its proof which uses Wronskians of vector-valued $\theta$-functions. This complements the work of A. Milas towards modular Wronskians and denominator identities.

Accepted for publication in Research in Number Theory