 
Summary: A CUSPIDALITY CRITERION FOR THE EXTERIOR SQUARE
TRANSFER OF CUSP FORMS ON GL(4)
MAHDI ASGARI AND A. RAGHURAM
Dedicated to Freydoon Shahidi on the occasion of his sixtieth birthday
Abstract. For a cuspidal automorphic representation of GL(4, A), H. Kim proved
that the exterior square transfer 2
is nearly an isobaric automorphic representation of
GL(6, A). In this paper we characterize those representations for which 2
is cuspidal.
1. Introduction and statement of the main theorem
Let F be a number field whose ad`ele ring we denote by AF . Let G1 and G2 be two
connected reductive linear algebraic groups over F, with G2 quasisplit over F, and let
LG1 and LG2 be the corresponding Lgroups. Given an Lhomomorphism r : LG1 LG2,
Langlands principle of functoriality predicts the existence of a transfer r() of the L
packet of an automorphic representation of G1(AF ) to an Lpacket r() of automorphic
representations of G2(AF ). Now assume that G2 is a general linear group. We note that an
Lpacket for a general linear group is a singleton set. For applications of functoriality one
needs to understand the image and fibers of the correspondence r(). In particular, it
is necessary to understand what conditions on ensure that the transfer r() is cuspidal.
The main aim of this paper is to describe a cuspidality criterion for the transfer of
