A Pieri Formula for the Characters of Complex Simple Lie Algebras

A Pieri formula is presented for the characters of complex simple Lie algebras of arbitrary Dynkin type, providing the decomposition of the tensor product of a general irreducible representation with one taken from a particular subclass of very small representations. The class of very small irreducible representations under consideration exceeds the minuscule and quasi-minuscule representations and includes in particular all fundamental representations in the case of a classical Lie algebra.