A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)

TL;DR

This paper characterizes when the exterior square transfer of a cuspidal automorphic representation on GL(4) remains cuspidal, providing a criterion that deepens understanding of automorphic transfers and their properties.

Contribution

It introduces a cuspidality criterion for the exterior square transfer of GL(4) cusp forms, clarifying when the transfer preserves cuspidality.

Findings

Identifies conditions under which heta^2 ext{Pi} is cuspidal.

Provides a characterization that distinguishes cuspidal from non-cuspidal transfers.

Enhances understanding of automorphic transfer properties on GL(4).

Abstract

For a cuspidal automorphic representation \Pi of GL(4,A), H. Kim proved that the exterior square transfer \wedge^2\Pi is an isobaric automorphic representation of GL(6,A). In this paper we characterize those representations \Pi for which \wedge^2\Pi is cuspidal.