Representation Theory and Automorphic Forms

Speh教授建议研究关于可约李群G的不可约表示限制到对称子群H的几个问题。她建议得到限制某类酉群表示到对称子群的分支公式。实数阶1的群的补级数表示的限制也将被考虑到相同类型的子群。这两个问题都适用于自同构型和算术群的上同调。她还建议继续研究由对称子群定义的广义模符号和周期积分。她进一步建议与D.Barbasch一起研究E型剩余谱中的表示。约化李群的表示被用来描述物理系统、微分方程、几何对象的对称性。或者数论中的一个问题。Speh教授建议研究“对称性的破缺”，即考虑一个不同的、通常较小的对称性群的问题。这个问题的特殊情况在物理学中已经被考虑过了。这项研究的智力价值在于更好地理解了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.