Representation Theory of Lie Groups

该项目设想在表征理论的广泛框架内对三个不同领域进行调查。第一组问题涉及康采维奇的形变量子化及其与李氏理论的联系。第二个研究领域是通过小的么正表示的显式模型研究theta-对应的可能推广及其张量积的研究。第三个研究主题是多元特殊函数的麦克唐纳-切莱德尼克理论。表示理论是现代数学的中心学科，因此受到代数、分析、数论和物理等不同学科自然产生的问题的启发。粗略地说，当数学问题具有一组对称性时，群的表示理论在考虑中起着潜在的关键作用。事实上，这个主题的种子在于伽罗瓦关于多项式方程对称性的工作；斯波胡斯关于微分方程对称性的工作；以及牛顿、傅立叶、爱因斯坦、维格纳和其他人关于物理系统对称性的工作。

AbstractSahiThe project envisages investigations in three different areas within the broad framework of representation theory. The first set of questions is related to Kontsevich's deformation quantization and its connections with Lie theory. The second area of investigation is the study of possible generalizations of the theta-correspondence via explicit models of small unitary representations and the study of their tensor products. The third topic of research is the Macdonald-Cherednik theory of multivariate special functions.Representation theory is a central discipline in modern mathematics and is therefore inspired by questions that arise naturally in diverse subjects such as algebra, analysis, number theory and physics. Roughly speaking whenever a mathematical problem possesses a group of symmetries, the representation theory of the group plays a potentially key role in the considerations. Indeed, the seeds of the subject lie in the work of Galois on the symmetries of polynomial equations; of Spohus Lie on the symmetries of differential equations; and of Newton, Fourier, Einstein, Wigner and others on the symmetries of physical systems.