Asai cube L-functions and the local Langlands correspondence

Guy Henniart, LUIS ALBERTO LOMELÍ

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)247-269
Number of pages23
JournalJournal of Number Theory
Volume221
DOIs
StatePublished - Apr 2021
Externally publishedYes

Keywords

  • Asai representation
  • Automorphic L-functions
  • Langlands correspondence
  • Local factors

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