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.References
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Additional Information
- A. Matsuo
- Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan
- MR Author ID: 276159
- Email: matsuo@ms.u-tokyo.ac.jp
- A. P. Veselov
- Affiliation: Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom — and — Moscow State University, Moscow 119899, Russia
- MR Author ID: 194169
- Email: A.P.Veselov@lboro.ac.uk
- Received by editor(s): January 9, 2017
- Published electronically: August 1, 2017
- Additional Notes: The work of the first author was partially supported by JSPS KAKENHI Grant Number JP26610004
- Communicated by: Jerzy Weyman
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5123-5130
- MSC (2010): Primary 17B20; Secondary 17B08
- DOI: https://doi.org/10.1090/proc/13819
- MathSciNet review: 3717942