In mathematics, restricted root systems, sometimes called relative root systems, are the root systems associated with a symmetric space.
The associated finite reflection group is called the restricted Weyl group.
The restricted root system of a symmetric space and its dual can be identified.
For symmetric spaces of noncompact type arising as homogeneous spaces of a semisimple Lie group, the restricted root system and its Weyl group are related to the Iwasawa decomposition of the Lie group.
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