Small principal series and exceptional duality for two simply laced exceptional groups

Abstract

We use the notion of rank defined in an earlier paper (2007) to introduce and study two correspondences between small irreducible unitary representations of the split real simple Lie groups of types E n , where n ∈ {6, 7}, and two reductive classical groups. We show that these correspondences classify all of the unitary representations of rank two (in the sense of our earlier paper) of these exceptional groups. We study our correspondences for a specific family of degenerate principal series representations in detail.