Abstract
We study bosonic tau functions in relation with the charged free bosonic fields. It is proved that up to a constant the only tau function in the Fock space ℳ is the vacuum vector, and some tau functions are given in the completion \(\widetilde{\cal M}\) by using Schur functions. We also give a new proof of Borchardt’s identity and obtain several q-series identities by using the boson-boson correspondence.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11531004) and the Simons Foundation (Grant No. 523868). The authors thank the anonymous referees whose comments have greatly improved this paper.
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Jing, N., Li, Z. Tau functions of the charged free bosons. Sci. China Math. 63, 2157–2176 (2020). https://doi.org/10.1007/s11425-019-1735-4
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DOI: https://doi.org/10.1007/s11425-019-1735-4