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In this paper we consider some global constructions of liftings ofautomorphic representations attached to some commuting pairs in the exceptionalgroup $F_4$. We consider two families of integrals. The first uses the minimalrepresentation on the double cover of $F_4$, and in the second we considerexamples of integrals of descent type associated with unipotent orbits of$F_4$.

On Certain Global Constructions of Automorphic Forms Related to Small Representations of $F_4$