  This paper addresses the representation theory of the insertion-elimination
Lie algebra, a Lie algebra that can be naturally realized in terms of
tree-inserting and tree-eliminating operations on rooted trees. The
insertion-elimination algebra admits a triangular decomposition in the sense of
Moody and Pianzola, and thus it is natural to define a Whittaker module
corresponding to a given algebra homomorphism. Among other results, we show
that the standard Whittaker module is simple given certain constraints on the
corresponding algebra homomorphism.
