Universal formula for Hilbert series of minimal nilpotent orbits

A. Matsuo; A. P. Veselov

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arXiv · 1602.00350

Universal formula for Hilbert series of minimal nilpotent orbits

A. Matsuo·A. P. Veselov

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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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BibTeX RIS

A. Matsuo, A. P. Veselov. 2016-02-01. Universal formula for Hilbert series of minimal nilpotent orbits. https://arxiv.org/abs/1602.00350

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