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Description of root systems with given Weyl group
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 397-402 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the description of generalized root systems with a given Weyl group. This problem arises in connection with the classification of infinite-dimensional Lie algebras and in the study of discrete groups generated by reflections. A criterion for the existence of a root system for a given discrete group generated by reflections and an algorithm of describing all root systems with a given Weyl group are obtained. 
@article{MZM_1998_64_3_a6,
     author = {I. I. Kotova},
     title = {Description of root systems with given {Weyl} group},
     journal = {Matemati\v{c}eskie zametki},
     pages = {397--402},
     year = {1998},
     volume = {64},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a6/}
}
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I. I. Kotova. Description of root systems with given Weyl group. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 397-402. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a6/

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