We show that the Hilbert series of the projective variety $X=P(O_{ min}),$ corresponding to the minimal nilpotent orbit $\mathcal O_{ min},$ 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 ${ }_{ 4}F_{ 3}.$ A universal formula for the degree of $X$ is then deduced.
Categories: math.RT