Rationality of the generalized binomial coefficients for a multiplicity free action

LetVbe a finite dimensional Hermitian vector space andKbe a compact Lie subgroup ofU(V) for which th representation ofKonC[V] is multiplicity free. One obtains a canonical basis {pα} for the spaceC[VR]kofK-invariant polynomials on VRand also a basis {q's. The polynomialpα's yields the homogeneous component of highest degree inqα. The coefficient that express theqα's in terms of thepβ's are the generalized binomial coeffficients of Yan. The main result in this paper shows tht these numbers are rational.