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Dichotomy for generic supercuspidal representations of G2

  • Gordan Savin (a1) and Martin H. Weissman (a2)

Abstract

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 or PGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3. 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 PGSp 6.

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References

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Dichotomy for generic supercuspidal representations of G2

  • Gordan Savin (a1) and Martin H. Weissman (a2)

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