论文标题
Hecke代数$ p $ - 亚种还原群体和伯恩斯坦街区的当地兰兰兹信件
Hecke algebras for $p$-adic reductive groups and Local Langlands Correspondence for Bernstein blocks
论文作者
论文摘要
我们研究了还附加到还原性$ p $ - 亚种组的伯恩斯坦组成部分的内态代数，并使用适当的增强的$ l $ -parameters构建了当地的Langlands对应关系，并使用某些“ Desiderata”属性用于LLC用于LLC的超级努力代表LLC。我们将LLC的多个应用程序应用于各种还原群，并在一般线性基团方面支持了伯恩斯坦障碍。 特别是，对于分裂异常组$ g_2 $的最大抛物线的Levi亚组，我们计算相应的Hecke代数的显式权重函数，并表明它们满足了Lusztig的猜想。同一位作者使用$§4$的一些结果来构建\ cite {ax-llc}的完整本地兰兰兹通讯。此外，我们还证明了与Levi亚组的常规超矛盾表示相连的Bernstein组件的深度零病例结果。
We study the endomorphism algebras attached to Bernstein components of reductive $p$-adic groups and construct a local Langlands correspondence with the appropriate set of enhanced $L$-parameters, using certain "desiderata" properties for the LLC for supercuspidal representations of proper Levi subgroups. We give several applications of our LLC to various reductive groups with Bernstein blocks cuspidally supported on general linear groups. In particular, for Levi subgroups of maximal parabolic of the split exceptional group $G_2$, we compute the explicit weight functions for the corresponding Hecke algebras, and show that they satisfy a conjecture of Lusztig's. Some results from $§4$ are used by the same authors to construct a full local Langlands correspondence in \cite{AX-LLC}. Moreover, we also prove a reduction to depth zero case result for the Bernstein components attached to regular supercuspidal representations of Levi subgroups.
