Geodesic
Restricted Roots and Restricted Form of the Weyl Dimension Formula for Spherical Varieties
Journal of Lie theory, Tome 23 (2013) no. 1, pp. 257-311.

Voir la notice de l'article provenant de la source Heldermann Verlag

We study in this paper the restricted roots for a class of spherical homogeneous spaces of semisimple groups which includes simply connected symmetric spaces. For these spaces we give a detailed description (case by case) of the set of roots of the group associated with each restricted root of the space (the "nest" of the restricted root). As an application, we obtain a refinement of the Weyl dimension formula in the case of spherical representations, expressing the dimension as a product over the set of indivisible positive restricted roots.
Classification : 14M27, 17B10, 20G20, 22E46
Mots-clés : Spherical variety, symmetric space, restricted root system, Weyl dimension formula 
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     title = {Restricted {Roots} and {Restricted} {Form} of the {Weyl} {Dimension} {Formula} for {Spherical} {Varieties}},
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S. Gindikin; R. Goodman . Restricted Roots and Restricted Form of the Weyl Dimension Formula for Spherical Varieties. Journal of Lie theory, Tome 23 (2013) no. 1, pp. 257-311. http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a14/