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

## TL;DR

This paper extends Macdonald's identity for rak{sl}_n to a two-variable form using Wronskians of vector-valued ta-functions, connecting to modular forms and denominator identities.

## Contribution

It introduces a new two-variable extension of Macdonald's identity for rak{sl}_n, employing Wronskians of vector-valued ta-functions.

## Key findings

- Provides a novel two-variable identity for rak{sl}_n
- Uses Wronskians of vector-valued ta-functions in proof
- Connects to modular Wronskians and denominator identities

## 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.