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Universal formula for the Hilbert series of minimal nilpotent orbits

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journal contribution
posted on 16.06.2017 by A. Matsuo, Alexander Veselov
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.

Funding

The work of AM was partially supported by JSPS KAKENHI Grant Number JP26610004.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the AMS

Citation

MATSUO, A. and VESELOV, A.P., 2017. Universal formula for the Hilbert series of minimal nilpotent orbits. Proceedings of the American Mathematical Society, 145, pp. 5123-5130.

Publisher

© American Mathematical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

09/05/2017

Publication date

2017-08-01

Notes

First published in Proceedings of the American Mathematical Society 145 (August 2017), published by the American Mathematical Society. © 2017 American Mathematical Society.

ISSN

0002-9939

eISSN

1088-6826

Language

en

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