Pro-p-Iwahori Hecke代数与模p局部朗兰兹纲领

本项目主要运用余中心理论来研究Pro-p-Iwahori Hecke代数及其表示的某些重要性质，并将相应的结果运用到模p局部朗兰兹对应中。具体来讲，我们将研究与p-进约化群G的不可约可容性表示相对应的Pro-p-Iwahori Hecke代数的单模。另外，我们将具体构造非分歧酉群U(2,1)的模p局部朗兰兹对应。同时，我们将构造酉群U(p,q)的pro-p-Iwahori Hecke代数的超奇异模。

In this project, we mainly use cocenter representation theory to obtain some important properties of pro-p-Iwahori Hecke algebras and their representations. Then we apply those results on pro-p-Iwahori Hecke algebras to mod p local Langlands program. More specifically, we will consider those simple modules which correspond to the irreducible admissible representations of p-adic reductive group G. Moreover, we will construct the mod p local Langlands correspondence for the unramified unitary group U(2,1), and for the unitary group U(p,q), we will construct the supersingular modules of the corresponding pro-p-Iwahori Hecke algebra.