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

Restricted Roots and Restricted Form of Weyl Dimension Formula for Spherical Varieties
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球簇Weyl维数公式的受限根及受限形式

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发表时间：
2012
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通讯作者：
R. Goodman
R. Goodman
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文献类型：
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作者：
S. Gindikin;R. Goodman

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本文研究了一类包含单连通对称空间的半单群球面齐次空间的限制根。对于这些空间，我们给出了与空间的每个受限根(受限根的巢)相关的群的根集的详细描述(逐个例子)。作为应用，我们在球面表示的情况下得到了Weyl维度公式的改进，将维度表示为不可分的正限制根集合上的乘积。
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.