Modifications of bundles, elliptic integrable systems, and related problems

作者：Zotov A V^*; Smirnov A V

来源：Theoretical and Mathematical Physics, 2013, 177(1): 1281-1338.

DOI：10.1007/s11232-013-0106-1

• integrable system
• Painleve equation
• Hitchin system
• modification of bundles

We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik-Zamolodchikov-Bernard equations, classical and quantum R-matrices, monopoles, spectral duality, Painlev, equations, and the classical-quantum correspondence. For an SL(N,a",)-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations.

• 出版日期2013-10