Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups (with appendix by Jessica Fintzen)

Local Jacquet-Langlands correspondence for regular supercuspidal representations

We prove that Kaletha's local Langlands correspondence for regular supercuspidal representations gives the classical local Jacquet--Langlands correspondence due to Deligne--Kazhdan--Vigneras and Badulescu. As in a former joint paper with Oi, where a similar result is proved for the local Langlands correspondence for the general linear group, the key ingredients in our proof are the work of Bushnell--Henniart explicitly describing the local Jacquet--Langlands correspondence for essentially tame supercuspidal representations and its reinterpretation due to Tam in terms of Langlands--Shelstad's \…

超尖点表示的最新进展

Progrès récents sur les représentations supercuspidales

本文综述了非阿基米德局部域约化群超尖点表示的最新进展，重点介绍了在“驯顺”情形下其分类、特征标显式公式及局部 Langlands 对应的构造成果。

关于 $p$ 进群的 Hecke 代数的参数

On parameters of Hecke algebras for $p$-adic groups

本文证明了深度零类型的仿射 Hecke 代数与幂幺类型的同构，从而可显式计算其参数，并在特定假设下证明了 Lusztig 猜想关于任意 Bernstein 块与幂幺块参数一致的版本。

$\overline{\mathbb{Z}}[\frac{1}{p}]$-块的 tame $p$-adic 群的参数化与降维到深度零

Parametrization and reduction to depth zero of $\overline{\mathbb{Z}}[\frac{1}{p}]$-blocks of tame $p$-adic groups

研究通过参数化和降维到深度零的方法，揭示了 tame $p$-adic 群的 $\overline{\mathbb{Z}}[\frac{1}{p}]$-块结构与局部朗兰兹对应的关系。