Endoscopic Lifts from Pgl3 to G2 Wee Teck Gan and Gordan Savin
نویسنده
چکیده
We determine essentially completely the theta correspondence arising from the dual pair PGL3 × G2 ⊂ E6 over a p-adic field. Our first result determines the theta lift of any non-supercuspidal representation of PGL3 and shows that the lifting respects Langlands functoriality. Our second result shows that the theta lift θ(π) of a (non-self-dual) supercuspidal representation π of PGL3 is an irreducible generic supercuspidal representation of G2; we also determine θ(π) explicitly when π has depth zero.
منابع مشابه
Global Endoscopic Lifts from Pgl3 to G2 Wee Teck Gan and Gordan Savin
Let π be a cuspidal automorphic representation of PGL3(A) (where A is the adele ring of F ). The functoriality conjecture of Langlands predicts that, via the inclusion γ of dual groups, there is a global L-packet L(π) of G2 associated to π. Indeed, for each place v of F , there should be a local L-packet L(πv) of G2(Fv). It is expected that L(πv) contains a unique generic representation σ(πv). ...
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