Bruht-Tits Buildings and the Representation Theory of a Reductive P-adic Group

摘要MoyMoy将研究约化p-进群表示理论中的两个问题。在第一个项目中，莫伊将研究利用Bruhat-Tits建立的约化群在其表示理论和调和分析中的应用。Moy将用两种不同的方法研究非常古老的基本猜想，即每个不可约的超尖球面表示都是由一个开紧的模中心子群紧导出的。这两种方法中的第一种是基于Moy和Prasad早期联合工作的推广，在超尖球面表示深度为零的情况下证明了猜想。第二种方法是证明任何不包含类指子群的尖角表示的不可约光滑表示一定有一个非零Jacquet函子。这两种方法都涉及Bruhat-Tits大楼。同样，作为第一个项目的一部分，莫伊将把他与巴巴施的合作扩展到其他扭曲的情况，该工作给出了关于轨道积分的豪猜想的一个新证明。对于第二个项目，Moy将研究群G上G-不变本质紧分布的显式构造。

AbstractMoyMoy will investigate two topics in the representation theory of reductive p-adic groups. In the first project, Moy will study the use of the Bruhat-Tits building of a reductive group in its representation theory and harmonic analysis. Moy will investigate by two different methods the very old fundamental conjecture that every irreducible supercuspidal representation is compactly induced from an open compact modulo center subgroup. The first of these two methods is based upon extension of earlier joint work of Moy and Prasad which proved the conjecture in the case the supercuspidal representation has depth zero. The second method would be to show that any irreducible smooth representation which does not contain a cuspidal representation of a parahoric subgroup must have a nonzero Jacquet functor. Both these methods involve the Bruhat-Tits building. Also as part of the first project, Moy will extend his joint work with Barbasch which gave a new proof of the Howe conjecture on orbital integrals to other twisted cases. For the second project, Moy will investigate explicit construction of G-invariant essentially compact distributions on the group G.