The exceptional Lie groups of type E_6, E_7, and E_8 have forms of split rank 4 which admit a quaternionic structure. Each contains a dual pair of the form G x G', where G is of type G_2, and G' has split rank 1. Restricting the minimal representation of the ambient group to this dual pair, one obtains an exceptional theta correspondence in which quaternionic representations (a la Gross--Wallach) play a crucial role.
In this talk we shall review quaternionic representations and explain the key properties that allow us to establish some new results about the above correspondence. Time permitting, we will discuss some applications in the setting of automorphic forms and functorial liftings. This is joint work with H.-Y. Loke and G. Savin.