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

美意量子群及孤子方程解合作研究

• 批准号: 9015923
• 负责人: Victor Kac
• 金额: $ 1.3万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-02-15 至 1992-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9015923&HistoricalAwards=false
• 关键词: U.S.; Italy; Cooperative; Research; Quantum

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.

该奖项将支持麻省理工学院的 Victor Kac 教授对意大利比萨进行为期四个月的访问，与比萨师范学院的 Corrado DeConcini 教授一起开展研究。 这两位数学家打算研究统一根的量子群以及孤子方程异常层次结构的准周期解。 最近有大量关于量子群 Uq(g) 的工作，其中 g 是泛型 q 的有限维简单李代数。 对于 q = 1 的根，Uq(g) 的属性有显着不同。 研究人员对这种情况下 Uq(g) 中心的结构特别感兴趣。 在孤子方程的准周期解领域，由于 Krichever 构造，黎曼 theta 函数被视为 Kadomtsev-Petviashvili (KP) 方程的解。 这一结果已被扩展以表明 Prym theta 函数也是 B 型 KP 方程的解。拟议的联合工作将尝试表明一些进一步的推广，例如 Prym-Tjurin theta 函数，也将成为孤子方程其他特殊层次结构的解。