Representation Theory and Automorphic Forms

Speh教授提出要研究关于约化李群G的不可约表示限制为对称子群H的几个问题。 她建议获得一个分支公式的限制某些类的酉表示的对称子群。还将考虑真实的秩为一的群的互补级数表示对同类型子群的限制。这两个问题都可以应用于自守形式和算术群的上同调。她还建议继续调查广义模符号和周期积分定义的对称子群。她建议进一步研究与D。Barbasch的表示在剩余频谱的E型。表示的约化李群是用来描述对称性的物理系统，微分方程，几何对象。或者是数论中的问题Speh教授建议研究“对称性破缺”，即考虑一个不同的，通常较小的对称群的问题。这个问题的特殊情况在物理学中已被考虑过。 这项研究的智力价值是更好地理解自然界和数学中的对称性。

AbstractSpehProfessor Speh proposes to work on several problems concerning the restriction of an irreducible representation of a reductive Lie group G to a symmetric subgroup H. She proposes to obtain a branching formula for the restriction of certain class of unitary representations to a symmetric subgroup. The restriction of complementary series representations of groups of real rank one to subgroups of the same type will also be considered. Both of these problems have applications to automorphic forms and the cohomology of arithmetic groups. She also proposes to continue to investigate generalized modular symbols and period integrals defined by symmetric subgroups. She proposes furthermore to investigate together with D. Barbasch the representations in the residual spectrum of type E.Representations of reductive Lie groups are used to describe the symmetry of a physical system, a differential equation, a geometric object. or a problem in Number Theory. Professor Speh proposes to study the "breaking of the symmetry", i.e consider the problem for a different, usually smaller, symmetry group. Special cases of this problem have been consider in physics. The intellectual merit of this research is a better understanding of symmetries in nature and in mathematics.