On endoscopic decomposition of certain depth zero representations

Endoscopic decomposition of characters of certain cuspidal representations

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Endoscopic character identities for depth-zero supercuspidal L-packets

We prove the conjectural endoscopic transfer of L-packets for the local Langlands correspondence for pure inner forms of unramified p-adic groups and depth-zero parameters established by DeBacker and Reeder. More precisely, we show that under mild conditions on the residual characteristic, endoscopic induction identifies an unstable character of such an L-packet with the stable character of the corresponding endoscopic L-packet.

椭圆Fargues-Scholze L-包的内窥分解

Endoscopic decomposition of elliptic Fargues-Scholze L-packets

本文证明了对应椭圆L-参数的Fargues-Scholze局部L-包具有内窥分解，并基于Arthur及近期工作将此分解推广至复数及特征零代数闭域上。

Sally-Shalika 特征标公式与 $\mathrm{SL}_2$ 的内窥特征标恒等式的比较

Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$

本文比较了 $\mathrm{SL}_2(F)$ 深度为零超尖 $L$-包的内窥特征标恒等式与 Sally-Shalika 经典公式，重点揭示大小为 $4$ 的 $L$-包中范数 $1$ 群 $H_1,H_2,H_3$ 的关键作用。

内窥分解与Hausel-Thaddeus猜想

Endoscopic decompositions and the Hausel-Thaddeus conjecture

本文构造算子连接不同秩与亏格的稳定Higgs丛模空间上同调，经数值特化恢复Hausel-Thaddeus拓扑镜像对称猜想，并利用消没圈函子联系Hitchin fibration分解定理给出新证明。

Depth preserving property of the local Langlands correspondence for quasi-split classical groups in a large residual characteristic

For a quasi-split classical group over a p-adic field with sufficiently large residual characteristic, we prove that the maximum of depth of representations in each L-packet equals the depth of the corresponding L-parameter. Furthermore, for quasi-split unitary groups, we show that the depth is constant in each L-packet. The key is an analysis of the endoscopic character relation via harmonic analysis based on the Bruhat--Tits theory. These results are slight generalizations of a result of Ganapathy and Varma.