MATSUO, A. and VESELOV, A.P., 2017. Universal formula for Hilbert series of minimal nilpotent orbits. Proceedings of the American Mathematical Society, In Press.
We show that the Hilbert series of the projective variety X = P(Omin), corresponding to the minimal nilpotent orbit Omin, is
universal in the sense of Vogel: it is written uniformly for all simple Lie algebras in terms of Vogel’s parameters α, β, γ and represents a special case of the generalized hypergeometric function 4F3. A universal formula for the degree of X is then deduced.
This paper is closed access until it is published.
The work of AM was partially supported by JSPS KAKENHI Grant Number JP26610004.