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Gaudin subalgebras and wonderful models
journal contribution
posted on 2016-01-08, 10:10 authored by Leonardo Aguirre, G. Felder, Alexander VeselovAlexander VeselovGaudin 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 SeriesPages
1 - 15Citation
AGUIRRE, L, FELDER, G. and VESELOV, A.P., 2016. Gaudin subalgebras and wonderful models. Selecta Mathematica, 22 (3), pp. 1057–1071.Publisher
© SpringerVersion
- 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
2015-11-26Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00029-015-0213-y.ISSN
1022-1824eISSN
1420-9020Publisher version
Language
- en