ar X iv : 0 90 8 . 33 40 v 1 [ m at h . R T ] 2 3 A ug 2 00 9 DICHOTOMY FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF G
نویسندگان
چکیده
The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3 when p 6= 2. This correspondence arises from theta correspondences in E6 and E7, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irreducible representations of G2 to a single conjecture about the parameterization for PGSp6, when p 6= 2.
منابع مشابه
ar X iv : 0 90 8 . 33 40 v 2 [ m at h . R T ] 3 0 A ug 2 00 9 DICHOTOMY FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF G
The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3. This corresponden...
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