Journal of the Ramanujan Mathematical Society

Abstract

Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F. We prove functoriality from globally generic cuspidal representations of GU(2, 2)(𝔸_F ) to automorphic representations of GL₆(𝔸_F ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F, the twisted exterior square map reduces to the usual exterior square map from GL₄(𝕔) to GL₆(𝕔). We also discuss functoriality for the twisted symmetric fourth power map and discuss its relation with functoriality of the twisted exterior square.

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