Mathematical Sciences: Representation Theory and Automorphic Forms

9401176 Speh/Barbasch Speh将继续她与Rohlfs关于倒钩上同源的联合研究。她也将研究局部对称空间的解析扭转。在联合工作中，PI将研究分裂正交群和辛群的残差谱。Barbasch将继续他对真实群体的无能表征的研究，特别是他们的性格理论和统一性。他也将研究分裂p进群的球酉对偶。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。＊＊＊

9401176 Speh/Barbasch Speh will continue her joint work with Rohlfs on cuspidal cohomology. She also will investigate the analytic torsion of locally symmetric spaces. In joint work the PI's will study the residual spectrum of the split orthogonal and symplectic group. Barbasch will continue his research on unipotent representations for real groups, in particular their character theory and unitarity. He also will study spherical unitary dual for split p- adic groups. 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. ***