Geodesic
Bethe Manifolds Associated with Classical Root Systems
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 709-717 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_2007_82_5_a5,
     author = {V. V. Meshcheryakov},
     title = {Bethe {Manifolds} {Associated} with {Classical} {Root} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {709--717},
     year = {2007},
     volume = {82},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a5/}
}
TY  - JOUR
AU  - V. V. Meshcheryakov
TI  - Bethe Manifolds Associated with Classical Root Systems
JO  - Matematičeskie zametki
PY  - 2007
SP  - 709
EP  - 717
VL  - 82
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a5/
LA  - ru
ID  - MZM_2007_82_5_a5
ER  - 
%0 Journal Article
%A V. V. Meshcheryakov
%T Bethe Manifolds Associated with Classical Root Systems
%J Matematičeskie zametki
%D 2007
%P 709-717
%V 82
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a5/
%G ru
%F MZM_2007_82_5_a5
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/

[1] V. A. Golubeva V. P. Leksin, “Heisenberg–Weyl operator algebras associated to the models of Calogero–Sutherland type and isomorphism of rational and trigonometric models”, J. Math. Sci. (N. Y.), 98:3 (2000), 291–318 | DOI | MR | Zbl

[2] Dzh. Khamfris, Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003 | MR | Zbl

[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