Simple wild L-packets

Epipelagic L-packets and rectifying characters

We provide an explicit construction of the local Langlands correspondence for general tamely-ramified reductive p-adic groups and a class of wildly ramified Langlands parameters. Furthermore, we verify that our construction satisfies the expected properties of such a correspondence. More precisely, we show that each L-packet we construct admits a parameterization in terms of the Langlands dual group, contains a unique generic element for a fixed Whittaker datum, satisfies the formal degree conjecture, is compatible with twists by central and cocentral characters, provides a stable virtual char…

Simple supercuspidal L-packets of quasi-split classical groups

In this paper, for quasi-split classical groups over p-adic fields, we determine the L-packets consisting of simple supercuspidal representations and their corresponding L-parameters, under the assumption that p is not equal to 2. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.

Simple supercuspidal L-packets of symplectic groups over dyadic fields

We consider the symplectic group $\mathrm{Sp}_{2n}$ defined over a $p$-adic field $F$, where $p=2$. We prove that every simple supercuspidal representation (in the sense of Gross--Reeder) of $\mathrm{Sp}_{2n}(F)$ corresponds to an irreducible $L$-parameter under the local Langlands correspondence for $\mathrm{Sp}_{2n}$ established by Arthur.

On the uniqueness of generic representations in an $L$-packet

In this paper, we give a simple and short proof of the uniqueness of generic representations in an $L$-packet for a quasi-split connected classical group over a non-archimedean local field.

二进域上分裂特殊正交群的简单超尖点 L-包

Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields

本文研究 p-adic 分裂特殊正交群 SO_N 中含 Gross–Reeder 简单超尖点表示的 L-包，确定其结构及到一般线性群的内窥镜提升，并借助显式局部 Langlands 对应给出 L-参数的显式描述。

实紧简单群的离散系列L包

Discrete series L-packets for real reductive groups

本文基于Langlands和Shelstad的成果，系统阐述了实紧简单群离散系列L包的构造、参数化及特征关系，并引入新发展如归一化几何转移因子和双覆盖，简化了陈述与证明。