U.S.-Italy Cooperative Research on Quantum Groups and Solutions of Soliton Equations

该奖项将支持教授为期四个月的访问 麻省理工学院的维克托卡茨前往意大利的比萨开展研究，与 比萨高等师范学校的科拉多·德孔西尼教授。 这两位数学家打算在2010年研究量子群。 单位根与例外方程的拟周期解 孤立子方程的族 最近在量子方面有大量的工作 群Uq（g），其中g是有限维单李 代数，对于泛型q。 对于q = 1的根， Uq（g）有很大的不同。 的结构 对于这种情况，Uq（g）的中心特别感兴趣， 研究人员。 在拟周期解领域中， 孤子方程，感谢Krichever结构 黎曼θ函数被看作是Kadomtsev的解， Petviashvili（KP）方程。 这一成果得到了推广 证明了Prym θ函数也是KP的解 B型方程。 拟议的联合工作将试图 这表明，一些进一步的概括，例如，Prym- Tjurin theta函数，也将成为解决方案， 其他特殊的孤子方程族。

This award will support a four month visit by Professor Victor Kac of MIT to Pisa, Italy to carry out research with Professor Corrado DeConcini of the Scuola Normale in Pisa. The two mathmeticians intend to work on quantum groups at roots of unity and on quasiperiodic solutions of exceptional hierarchies of soliton equations. There has been a great deal of work recently on quantum groups Uq(g), where g is a finite-dimensional simple Lie algebra, for generic q. For q = root of 1 the properties of Uq(g) are dramatically different. The structure of the center of Uq(g) for this case is of particular interest to the researchers. In the area of quasiperiodic solutions of soliton equations, thanks to the Krichever constructions Riemann theta functions are seen as solutions of the Kadomtsev- Petviashvili (KP) equations. This result has been extended to show that Prym theta functions are also solutions of KP equations of type B. The proposed joint work will attempt to show that some further generalizations, for example the Prym- Tjurin theta functions, will also turn out to be solutions to other exceptional hierarchies of soliton equations.