Work

Dichotomy for generic supercuspidal representations of G 2

Year: 2011

Type: article

Abstract: The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G 2 over a p -adic field, one can associate a generic supercuspidal irreducible representation of either PGSp 6 or PGL 3 . We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G 2 and other representations of PGSp 6 and PGL 3 . This correspondence arises from theta correspondences in E 6 and E 7 , analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irreducible representations of G 2 to a single conjecture about the parameterization for PGSp 6 .

Source: Compositio Mathematica

DOI: 10.1112/s0010437x10005178

Authors: Gordan Savin, Martin H. Weissman

Institutions: University of Utah, University of California, Santa Cruz

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, American Institute of Mathematics, University of Michigan

Award: Representations, modular forms and Galois groups