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 GL1's or GL2'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 D4, with triality corresponding to E, and let L be its Levi subgroup with derived group ResE/FSL2. In this way we obtain Asai cube local factors attached to irreducible smooth representations of GL2(E); we prove that they are Weil-Deligne factors obtained via the local Langlands correspondence for GL2(E) and tensor induction from E to F. A consequence is that Asai cube γ- and ε-factors become stable under twists by highly ramified characters.
Original language | English |
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Pages (from-to) | 247-269 |
Number of pages | 23 |
Journal | Journal of Number Theory |
Volume | 221 |
DOIs | |
State | Published - Apr 2021 |
Keywords
- Asai representation
- Automorphic L-functions
- Langlands correspondence
- Local factors