UNIVERSAL FORMULA FOR THE HILBERT SERIES OF MINIMAL NILPOTENT ORBITS

摘要

We show that the Hilbert series of the projective variety X = P(O-min), corresponding to the minimal nilpotent orbit O-min, is universal in the sense of Vogel: it is written uniformly for all simple Lie algebras in terms of Vogel's parameters alpha, beta, gamma and represents a special case of the generalized hypergeometric function F-4(3). A universal formula for the degree of X is then deduced.