Abstract
Let n be an odd positive integer. In this short elementary note, we slightly extend Macdonald’s identity for \({{\mathfrak {s}}}{{\mathfrak {l}}}_{n}\) 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 Milas towards modular Wronskians and denominator identities.
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Acknowledgements
The author wishes to thank Ken Ono and Antun Milas for their support and interest in this note.
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Gazda, Q. An extension of Macdonald’s identity for \({{\mathfrak {s}}}{{\mathfrak {l}}}_{n}\). Res. number theory 5, 24 (2019). https://doi.org/10.1007/s40993-019-0163-0
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DOI: https://doi.org/10.1007/s40993-019-0163-0