Geodesic
Bethe Manifolds Associated with Classical Root Systems
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 709-717.

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The Calogero–Sutherland model [1] describes the state of a finite number of nonrelativistic particles on the circle (or on the hyperbola) interacting by the inverse-square law. For each classical root system (of the type $A_{n-1},B_n,C_n,D_n$), we describe the Bethe manifolds related to the Calogero–Sutherland model. In each case, the dimension of the manifold is calculated and its constitutive equations are given.
Keywords: root system, Bethe manifold, Calogero–Sutherland model, nonrelativistic particle, Weyl group. 
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V. V. Meshcheryakov. Bethe Manifolds Associated with Classical Root Systems. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 709-717. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a5/

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[3] Zh.-P. Serr, Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl

[4] N. Burbaki, Gruppy i algebry Li. Gruppy Kokstera i sistemy Titsa. Gruppy, porozhdennye otrazheniyami. Sistemy kornei., Mir, M., 1972 | MR | Zbl