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 wgan@math.ucsd.edu
a2 Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA savin@math.utah.edu

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

Abstract

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).


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