1. Gaudin subalgebras and wonderful models
- Author
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Aguirre, Leonardo, Felder, Giovanni, and Veselov, Alexander P.
- Subjects
Mathematics::Algebraic Geometry ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Mathematics::Quantum Algebra ,Primary 81R12, Secondary 20F55, 14H70, 14N20 ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Mathematics::Representation Theory ,Mathematical Physics - 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., Comment: 13 pages, 2 figures; added detailed description of the B_2 and B_3 cases in the new version
- Published
- 2014
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