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 gamma- and epsilon-factors become stable under twists by highly ramified characters.