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arXiv · 1904.10191

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

Quentin Gazda
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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.

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Quentin Gazda. 2019-04-23. An extension of Macdonald's identity for $\mathfrak{sl}_n$. https://doi.org/10.1007/s40993-019-0163-0

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