Gaudin subalgebras and wonderful models
Mathematical Physics
2015-01-06 v2 math.MP
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.
Keywords
Cite
@article{arxiv.1409.2052,
title = {Gaudin subalgebras and wonderful models},
author = {Leonardo Aguirre and Giovanni Felder and Alexander P. Veselov},
journal= {arXiv preprint arXiv:1409.2052},
year = {2015}
}
Comments
13 pages, 2 figures; added detailed description of the B_2 and B_3 cases in the new version