Mathematical Sciences: Discrete Spectrum of the Oscillator Representation and Applications

李将研究离散谱的限制， 振子表示为约化对偶对。 他将 把这项调查与研究的离散系列， 广义Stiefel流形 波阵面开始下沉， 离散序列的渐近分布将发挥至关重要的作用， 作用 所得结果将应用于构造酉 自守形式的经典群，包括那些与非 零上同调 它们还将用于构建 Rammanujan Dual。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身，特别是在分析和数字方面， 理论和理论物理学，特别是量子 力学和基本粒子物理学。

Li will study the discrete spectrum of the restriction of the oscillator representation to reductive dual pairs. He will relate this investigation to the study of the discrete series of generalized Stiefel manifolds. The wave front sets and asymptotic distributions of discrete series will play a vital role. The results will be applied to the construction of unitary automorphic forms on classical groups, including those with non- zero cohomology. They will also be used to construct elements of the Rammanujan Dual. 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.