Universal formula for the Hilbert series of minimal nilpotent orbits

Matsuo, A.; Veselov, A.

doi:10.1090/proc/13819

Universal formula for the Hilbert series of minimal nilpotent orbits
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by A. Matsuo and A. P. Veselov PDF

Proc. Amer. Math. Soc. 145 (2017), 5123-5130 Request permission

Abstract:

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.

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