Mathematical Sciences: Representations of Discrete Rational Nilpotent Groups

Pfeffer将经典的实数幂零李群的Kirillov理论推广到非i型环境。所涉及的基本技术是利用相关李代数对偶中的共伴随轨道闭包结构。这些闭包是李代数对偶子群的余集，它们湮灭了李代数中的理想。Pfeffer将研究共伴轨道闭包空间是否同胚于原始理想空间。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。

Pfeffer will extend the classical Kirillov theory of real nilpotent Lie groups to the non-type-I setting. The basic technique involved exploits the structure of co-adjoint orbits closures in the dual of the associated Lie algebra. These closures are cosets of subgoups of the Lie algebra dual which annihilate ideals in the Lie algebra. Pfeffer will investigate whether the space of co-adjoint orbit closures is homeomorphic to the primitive ideal space. 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.