经典群的内部提升与上皮层表示参数
Endoscopic liftings and parameters of epipelagic representations for classical groups
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中文总结 AI 辅助
本文利用 Mœglin 和 Bushnell-Kutzko 理论，确定了 $p$ 进经典群上皮层表示的内部提升，引入上皮层，并恢复 Reeder-Yu 的 Langlands 参数，推广了相关结果。
中文摘要 AI 辅助
设 $G$ 为 $p$ 进经典群（正交群、辛群或酉群），$\pi$ 为 $G$ 的 Reeder-Yu 意义上的上皮层表示。利用 Mœglin 的扩展尖点支撑理论和 Bushnell-Kutzko 的覆盖类型理论，我们明确地确定了 $\pi$ 到一般线性群的内部提升，其 Langlands 对偶将 $G$ 的对偶群表示为复矩阵群，该提升由 $\pi$ 的诱导类型给出，该类型扩展了由稳定泛函定义的第一 Moy-Prasad 滤过子群的特征。我们通过 Stevens 的斜半单层构造超尖点表示的方法来解释 $\pi$ 的诱导类型，并引入了我们称之为上皮层的东西，仅要求剩余特征 $p$ 为奇数。作为应用，我们重新证明了 M. Oi 关于 Gross-Reeder 意义上的拟分裂经典群的简单超尖点表示的内部提升的结果。最后，在 Galois 侧，我们证明了 Reeder-Yu 构造的 $G$ 的上皮层 Langlands 参数可以通过 Bushnell-Henniart 的可容许三元组的自对偶性和 L 群的内部嵌入来恢复。我们还建立了一些关于上皮层参数的相关结果，这些结果先前在 $p$ 的限制下得到证明，包括关于修正特征的奇偶性结果和与 Hiraga-Ichino-Ikeda 猜想相关的伴随 Swan 导子结果。
英文摘要
Let $G$ be a $p$-adic classical group (orthogonal, symplectic, or unitary) and $π$ be an epipelagic representation of $G$ in the sense of Reeder-Yu. Using Mœglin's theory of extended cuspidal supports and Bushnell-Kutzko's theory of covering types, we determine explicitly the endoscopic lift of $π$ to the general linear group, whose Langlands dual expresses the dual group of $G$ as a complex matrix group, in terms of the inducing type of $π$ that extends the character of the first Moy-Prasad filtration subgroup defined by a stable functional. We interpret the inducing type of $π$ via Stevens' construction of supercuspidal representations by skew semisimple strata and introduce what we will call epipelagic strata, requiring only that the residual characteristic $p$ be odd. As an application, we reprove M. Oi's results on the endoscopic lifts of simple supercuspidal representations, in the sense of Gross-Reeder, of quasi-split classical groups. Finally, on the Galois side, we show that the epipelagic Langlands parameters of $G$ constructed by Reeder-Yu can be recovered via the self-duality of Bushnell-Henniart's admissible triples and endoscopic embeddings of L-groups. We also establish some related results concerning epipelagic parameters that were previously proved under restrictions on $p$, including a parity result on rectifying characters and an adjoint Swan conductor result related to the Hiraga-Ichino-Ikeda conjecture.
发表机构
- Xiamen University Malaysia（厦门大学马来西亚分校）
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