Mathematical Sciences: Unitary Representations of Lie Groups and Derived Functor Modules

Salamanca Riba将研究群的不可约酉Harish-Chandra模与子群的一维酉表示衍生出的Zuckerman函子模之间的关系。她还将考虑对形而上学群的所有真酉表示进行分类的问题。特别是，她将考虑这些表示与元群的某些内部形式的一组幺正表示之间的Adams-Barbasch对应关系，并确定这些表示是否在该映射下进入Zuckerman函子模块。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

DMS-9510608 PI: Salamanca Riba Salamanca Riba will investigate the relation between certain irreducible unitary Harish-Chandra modules for a group and Zuckerman functor modules derived from a one dimensional unitary representation of a subgroup. She will also consider the problem of classifying all genuine unitary representations of the metaplectic group. In particular, she will consider the Adams-Barbasch correspondence between these representations and a set of unitary representations of certain inner forms of the metaplectic group and determine if the representations go to Zuckerman functor modules under this map. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.