Mathematical Sciences: Unitary Representations in Dolbeault Cohomology

Zierau将研究半单李群的椭圆伴轨道的奇异酉表示的实现，即Dolbeault上同调上的表示。他将用平方可积调和形式和轨道上不变的不定度规统一这些表示。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。

Zierau will investigate the realization of singular unitary representation associated to elliptic coadjoint orbits of a semisimple Lie group, i. e. representations on Dolbeault cohomology. He will unitarize these representations using square integrable harmonic forms and the invariant indefinite metric on the orbit. 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.