Abstract
Certain reductions of Hitchin systems of rank 2 and genera 2 and 3 are considered, which are shown to give integrable systems of two (respectively, three) interacting points on the line. It is shown that the reduced systems are particular cases of an integrable system related to the Lagrange interpolation polynomial. The admissibility of the reduction is proved using computer techniques. A reference to published software programs is given in the text.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. M. Buchstaber, Proc. Steklov Inst. Math. 294, 176–200 (2016).
K. Gawedzki and P. Tran-Ngog-Bich, J. Math. Phys. 41, 4695–4712 (2000). arXiv:hep-th/9803101.
B. van Geemen and E. Previato, Duke Math. J. 85, 659–683 (1996).
I. M. Krichever, Commun. Math. Phys. 229, 229–269 (2002). Hep-th/0108110.
O. K. Sheinman, Current Algebras on Riemann Surfaces (Walter de Gruyter, Berlin, 2012).
O. K. Sheinman, Theor. Math. Phys. 185 (3), 1816–1831 (2015).
O. K. Sheinman, Proc. Steklov Inst. Math. 290, 191–201 (2015).
O. K. Sheinman, Moscow Math. J. 15 (4), 833–846 (2015).
O. K. Sheinman, Russ. Math. Surv. 71 (1), 109–156 (2016). arXiv: 1602.04320.
A. N. Tyurin, Am. Math. Transl. Ser. 2 63, 245–279 (1967).
O. K. Sheinman, arXiv:1709.06803 [math-ph].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © O.K. Sheinman, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 3, pp. 254–256.
Rights and permissions
About this article
Cite this article
Sheinman, O.K. Certain Reductions of Hitchin Systems of Rank 2 and Genera 2 and 3. Dokl. Math. 97, 144–146 (2018). https://doi.org/10.1134/S1064562418020114
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562418020114