  A correction factor naturally arises in the theory of p-adic Kac--Moody
groups. In this paper, we expand the correction factor into a sum of
irreducible characters of the underlying Kac--Moody algebra. We derive a
formula for the coefficients, which lie in the ring of power series with
integral coefficients. In the case that the Weyl group is a universal Coxeter
group, we show that the coefficients are actually polynomials.
