• Source: Restricted root system

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.




See also


Satake diagram




References


Bump, Daniel (2004), Lie groups, Graduate Texts in Mathematics, vol. 225, Springer, ISBN 0387211543
Helgason, Sigurdur (1978), Differential geometry, Lie groups, and symmetric spaces, Academic Press, ISBN 0821828487
Onishchik, A. L.; Vinberg, E. B. (1994), Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras, Encyclopaedia of Mathematical Sciences, vol. 41, Springer, ISBN 9783540546832
Wolf, Joseph A. (2010), Spaces of constant curvature, AMS Chelsea Publishing (6th ed.), American Mathematical Society, ISBN 0821852825
Wolf, Joseph A. (1972), "Fine structure of Hermitian symmetric spaces", in Boothby, William; Weiss, Guido (eds.), Symmetric spaces (Short Courses, Washington University), Pure and Applied Mathematics, vol. 8, Dekker, pp. 271–357, ISBN 978-0-608-30568-4

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