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种表示的张量积的分解。 这些模型与经典群的局部θ-对应关系密切相关，并且可以被视为这种对应关系的自然推广。 结果预计有自然的全球类似物，与应用理论的自守形式。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。

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.