![]() | This article includes a
list of references,
related reading, or
external links, but its sources remain unclear because it lacks
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Lie groups and Lie algebras |
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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.
![]() | This article includes a
list of references,
related reading, or
external links, but its sources remain unclear because it lacks
inline citations. (May 2024) |
Lie groups and Lie algebras |
---|
![]() |
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.