Unipotent Representations and a Generalization of the Theta Correspondence

Sahi将为约化李群的小表示构建显式模型，并使用这些模型来研究这些表示的张量积的分解。这些模型与经典群的局部θ -对应密切相关，可以看作是这种对应的自然推广。该结果有望具有自然的全局类似物，并应用于自同构形式的理论。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。

Sahi will construct explicit models for small representations of reductive Lie groups, and use these models to study the decomposition of tensor products of such representations. These models are closely related to the local theta-- correspondence for classical groups, and may be regarded as a natural generalization of this correspondence. The results are expected to have natural global analogues, with applications to the theory of automorphic forms. 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.