TY - JOUR
T1 - Asai cube L-functions and the local Langlands correspondence
AU - Henniart, Guy
AU - LOMELÍ, LUIS ALBERTO
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/4
Y1 - 2021/4
N2 - 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.
AB - 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.
KW - Asai representation
KW - Automorphic L-functions
KW - Langlands correspondence
KW - Local factors
UR - http://www.scopus.com/inward/record.url?scp=85087759315&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2020.05.023
DO - 10.1016/j.jnt.2020.05.023
M3 - Article
AN - SCOPUS:85087759315
VL - 221
SP - 247
EP - 269
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -