Abstract Let F be a non-archimedean locally compact field. We study a class of Langlands-Shahidi pairs ( H , L ) , consisting of a quasi-split connected reductive group H over F and a Levi subgroup L which is closely related to a product of restriction of scalars of GL 1 's or GL 2 's. We prove the compatibility of the resulting local factors with the Langlands correspondence. In particular, let E be a cubic separable extension of F. We consider a simply connected quasi-split semisimple group H over F of type D 4 , with triality corresponding to E, and let L be its Levi subgroup with derived group Res E / F SL 2 . In this way we obtain Asai cube local factors attached to irreducible smooth representations of GL 2 ( E ) ; we prove that they are Weil-Deligne factors obtained via the local Langlands correspondence for GL 2 ( E ) and tensor induction from E to F. A consequence is that Asai cube γ- and e-factors become stable under twists by highly ramified characters.

中文翻译：

---

Asai 立方体 L 函数和局部朗兰兹对应

摘要 令 F 为非阿基米德局部紧场。我们研究了一类 Langlands-Shahidi 对 ( H , L ) ，由 F 上的准分裂连通还原群 H 和与 GL 1 或 GL 的标量限制的乘积密切相关的 Levi 子群 L 组成。 2 的。我们证明了由此产生的局部因素与朗兰兹对应的兼容性。特别地，令 E 是 F 的三次可分离扩展。我们考虑类型 D 4 的 F 上的单连通准分裂半单群 H，具有对应于 E 的试验，并令 L 是它的 Levi 子群，其具有派生群 Res E / F SL 2。通过这种方式，我们获得了附加到 GL 2 (E) 的不可约平滑表示上的 Asai 立方体局部因子；