Weil representations and cusp forms on unitary groups
Weil representations and cusp forms on unitary groups
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酉群上的韦尔表示和尖点形式
DOI：
10.1090/s0002-9904-1974-13646-3
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发表时间：
1974
影响因子：
1.3
通讯作者：
G. Lehrer
中科院分区：
文献类型：
--
作者：
G. Lehrer
介绍。在这篇文章中，我们宣布了有限酉群特征理论的一些结果。主要结果是将某个类函数/最大抛物线子群的限制分解为张量积。这个结果与[4]中一般线性群 GL («, q) 的结果类似，不同之处在于这里张量积的分量更加复杂。事实上，最大抛物型子群P的列维分解P= MH，其中M是低维酉群，H同构于“酉海森堡群”（见下文）；因此（参见[3]、[6]、[7]）获得 P 的“Weil 表示”，这些对于 J 的分解很有帮助。
Introduction. In this note we announce some results on the character theory of the finite unitary groups. The main result is the decomposition of the restriction of a certain class function/to a maximal parabolic subgroup as a tensor product. This result is analogous with those of [4] for the general linear group GL («, q), with the difference that the components of the tensor product are more complicated here. In fact, one has a Levi decomposition P= MH of the maximal parabolic subgroup P, where M is a unitary group of lower dimension, and H is isomorphic to the" unitary Heisenberg group"(see below); one therefore (see [3],[6],[7]) obtains" Weil representations" of P, and these are instrumental in the decomposition of J.