Mathematical Sciences: Beilinson-Ginsburg Duality for Semisimple Groups

盖拉尔教授将研究哈里什的结构- 半单李群的Chandra模 特别是他将 研究了表示代数与 扩张代数，并试图证明它们是对偶形式的 代数意义上的Beilinson和Ginsburg，猜想他 已经在特殊情况下验证过了。 本研究涉及群体表征理论。 群论基本上是研究对称性的。 采取 例如，当所讨论的系统在变化下不变时， 在空间原点的位置上，平移群 自然会出现。 虽然组是抽象对象，但特定的 情况需要具体的实现或“表示”， 对称群

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.