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Gaudin subalgebras and wonderful models

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Abstract

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.

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Notes

  1. We are grateful to Artie Prendergast-Smith, who explained this to us.

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Acknowledgments

We are grateful to I. Cherednik, M. Kapranov, T. Kohno and A. Prendergast-Smith for helpful and stimulating discussions. 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—SwissMAP”).

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Authors and Affiliations

  1. Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland

    Leonardo Aguirre & Giovanni Felder

  2. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    Alexander P. Veselov

  3. Moscow State University, Moscow, Russia

    Alexander P. Veselov

Authors
  1. Leonardo Aguirre
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  2. Giovanni Felder
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  3. Alexander P. Veselov
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Correspondence to Giovanni Felder.

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Aguirre, L., Felder, G. & Veselov, A.P. Gaudin subalgebras and wonderful models. Sel. Math. New Ser. 22, 1057–1071 (2016). https://doi.org/10.1007/s00029-015-0213-y

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