论文标题
真正的Pro- $ P $ IWAHORII-HECKE代数，Gelfand-Graev代表和某些申请
Genuine pro-$p$ Iwahori--Hecke algebras, Gelfand--Graev representations, and some applications
论文作者
论文摘要
我们研究了分裂线性还原组的中央覆盖物的Gelfand-Graev表示的Iwahori组件，并将我们的结果用于三种应用。实际上，从$ $ p $级别开始是有利的。因此，我们开始研究真正的Pro-P $ Iwahori-Hecke代数，建立Iwahori-Matsumoto和Bernstein演讲的结构。通过这种结构理论，我们首先描述了Gelfand-Graev表示的一部分，然后描述了更微妙的Iwahori部分。 对于第一个应用程序，我们将Gelfand-Graev表示与Sahi-Stokman-Venkateswaran的互惠表示相关，该代表从概念上实现了Weyl groude多个Dirichlet系列的Chinta-Gunnells动作。第二次，我们计算了常规未经委托系列的组成部分的惠特克维度；对于第三次，我们为单一未受到的原理系列做同样的事情。
We study the Iwahori-component of the Gelfand-Graev representation of a central cover of a split linear reductive group and utilize our results for three applications. In fact, it is advantageous to begin at the pro-$p$ level. Thus to begin we study the structure of a genuine pro-$p$ Iwahori-Hecke algebra, establishing Iwahori-Matsumoto and Bernstein presentations. With this structure theory we first describe the pro-$p$ part of the Gelfand-Graev representation and then the more subtle Iwahori part. For the first application we relate the Gelfand-Graev representation to the metaplectic representation of Sahi-Stokman-Venkateswaran, which conceptually realizes the Chinta-Gunnells action from the theory of Weyl group multiple Dirichlet series. For the second we compute the Whittaker dimension of the constituents of regular unramified principal series; for the third we do the same for unitary unramified principal series.
