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Gaudin subalgebras and wonderful models

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journal contribution
posted on 08.01.2016, 10:10 by Leonardo Aguirre, G. Felder, Alexander Veselov
Gaudin Hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin Hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini–Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes.

Funding

The work of APV was partly supported by the EPSRC (Grant EP/J00488X/1). The work of GF was partly supported by the Swiss National Science Foundation (National Centre of Competence in Research “The Mathematics of Physics—SwissMA)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Selecta Mathematica, New Series

Pages

1 - 15

Citation

AGUIRRE, L, FELDER, G. and VESELOV, A.P., 2016. Gaudin subalgebras and wonderful models. Selecta Mathematica, 22 (3), pp. 1057–1071.

Publisher

© Springer

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/

Publication date

2015-11-26

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00029-015-0213-y.

ISSN

1022-1824

eISSN

1420-9020

Language

en

Exports

Loughborough Publications

Keywords

Exports