Mathematical Sciences: Beilinson-Ginsburg Duality for Semisimple Groups

盖拉德教授将研究半简单李群的Harish- Chandra模的结构。特别是，他将研究表征代数和扩展代数的关系，并试图证明它们是Beilinson和Ginsburg意义上的对偶形式代数，他已经在特殊情况下验证了这一猜想。本研究涉及群体表征理论。群论基本上是对对称性的研究。举个例子，当所讨论的系统在空间原点位置的变化下是不变的，平移组自然产生。虽然群是抽象的对象，但特殊情况需要对称群的具体实现或“表示”。

Professor Gaillard will study the structure of Harish- Chandra modules for semisimple Lie groups. In particular he will study the relationship of the representation algebra and the extension algebra and try to show that they are dual formal algebras in the sense of Beilinson and Ginsburg, a conjecture he has verified already in special cases. This research involves the theory of group representations. Group theory is basically the study of symmetry. To take an example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group.