Mathematical Sciences: Microlocal Character Theory for Representations of Classical Lie Groups

Przebinda教授将研究分布特征 经典李群的不可约容许表示 从微观分析的角度来看。 这将在 Howe的还原对偶对理论的背景。 三 问题涉及该项目：（一）表征一个特殊的 类非常奇异表示这些群体，（二） 计算Howe's中诱导的波前集合的对应性 （三）调查研究; 由此产生的微分和微微分方程系统。 这项研究是在群体表征理论。 群论基本上是对称性理论。 采取 一个简单的例子，当所讨论的系统在一个 空间原点位置的变化， 翻译自然会出现。 虽然群体是抽象的， 对象，特殊情况需要具体实现或 对称群的“表示”。

Professor Przebinda will investigate distribution characters of irreducible admissable representations of classical Lie groups from the viewpoint of microlocal analysis. This will be done in the context of Howe's theory of reductive dual pairs. Three problems are involved in the project: (i) characterize a special class of very singular representations of these groups, (ii) calculate the correspondence of wavefront sets induced in Howe's correspondence of representations, and (iii) investigate the resulting system of differential and microdifferential equations. This research is in the theory of group representations. Group theory is basically the theory of symmetry. To take a simple 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.