Abstract
We study derivatives of Schur and tau functions from the view point of the Abel-Jacobi map. We apply the results to establish several properties of derivatives of the sigma function of an (n,s) curve. As byproducts we have an expression of the prime form in terms of derivatives of the sigma function and addition formulae which generalize those of Onishi for hyperelliptic sigma functions.
A part of the results in the present paper is reported in [16].
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Notes
- 1.
In the defining equation of c i in [12] c i should be corrected to c i /i.
References
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Acknowledgements
The authors would like to thank Yasuhiko Yamada for suggesting Theorem 3 and Yoshihiro Ônishi for a stimulating discussion. The first author is grateful to the organizers of the conference “Symmetries, Integrable Systems and Representations” held at Lyon, December 13–16, 2011, for financial support and kind hospitality. This research is partially supported by JSPS Grant-in-Aid for Scientific Research (C) No. 23540245.
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Dedicated to Michio Jimbo on his sixtieth birthday.
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Nakayashiki, A., Yori, K. (2013). Derivatives of Schur, Tau and Sigma Functions on Abel-Jacobi Images. In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_17
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