Mathematical Sciences: Harmonic Analysis on Reductive Groups

黄将研究半单李群的表示与其覆盖群的表示之间的关系。他将研究它们的酉对偶和Kazhdan-Lustig猜想之间的关系。他还将对称空间的调和分析的主要结果推广到一类他称之为极的齐次空间。这些都是齐次空间，在Dadok的意义上，限制伴随表示是极性的。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。

Huang will study the relationship between representations of a semisimple Lie groups and those of its covering group. He will investigate how their unitary duals and Kazhdan-Lustig conjecture are related. He will also extend the major results of harmonic analysis on symmetric spaces to a certain class of homogeneous spaces which he terms polar. These are homogeneous spaces for which the restricted adjoint representation is polar in the sense of Dadok. 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.