Gaudin subalgebras and wonderful models
journal contributionposted 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.
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)
- Mathematical Sciences