Character formulas and partition functions in higher dimensional conformal field theory

A discussion of character formulas for positive energy, unitary irreducible representations of the conformal group is given, employing Verma modules and Weyl group reflections. Product formulas for various conformal group representations are found. These include generalizations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not