Modifications of bundles, elliptic integrable systems, and related problems

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• 作者：A. V. Zotov (1) (2) (3)
  A. V. Smirnov (1) (4)
  
• 关键词：integrable system ; Painlevequation ; Hitchin system ; modification of bundles
• 刊名：Theoretical and Mathematical Physics
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：177
• 期：1
• 页码：1281-1338
• 全文大小：
• 作者单位：A. V. Zotov (1) (2) (3)
  A. V. Smirnov (1) (4)
  
  1. Institute for Theoretical and Experimental Physics, Moscow, Russia
  2. Moscow Institute for Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, Russia
  3. Steklov Mathematical Institute, RAS, Moscow, Russia
  4. Department of Mathematics, Columbia University, New York, USA
  
• ISSN：1573-9333

文摘

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, Painlevequations, and the classical-quantum correspondence. For an SL(N,)-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations.