Restricted Roots and Restricted Form of the Weyl Dimension Formula for Spherical Varieties

S. Gindikin; R. Goodman

doi:10.5802/jolt.727

S. Gindikin; R. Goodman

Journal of Lie Theory, Volume 23 (2013) no. 1, pp. 257-311

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.727

Classification: 14M27, 17B10, 20G20, 22E46
Keywords: 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}},
     journal = {Journal of Lie Theory},
     pages = {257--311},
     year = {2013},
     volume = {23},
     number = {1},
     doi = {10.5802/jolt.727},
     zbl = {1271.14079},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.727/}
}

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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, Volume 23 (2013) no. 1, pp. 257-311. doi: 10.5802/jolt.727

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