Compositio Mathematica

Endoscopic lifts from PGL3 to G2

Wee Teck Gan a1p1 and Gordan Savin a2
a1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA
a2 Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA

Article author query
gan w   [Google Scholar] 
savin g   [Google Scholar] 


We determine essentially completely the theta correspondence arising from the dual pair ${\it PGL}_3 \times G_2 \subset E_6$ 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 $\theta(\pi)$ of a (non-self-dual) supercuspidal representation $\pi$ of PGL3 is an irreducible generic supercuspidal representation of G2; we also determine $\theta(\pi)$ explicitly when $\pi$ has depth zero.

(Received April 8 2002)
(Accepted August 14 2002)

Key Words: theta correspondence; supercuspidal lifts.

Maths Classification

22E35; 22E50 (primary); 11F70 (secondary).

p1 Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA