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.
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, ISBN9783540546832
Wolf, Joseph A. (2010), Spaces of constant curvature, AMS Chelsea Publishing (6th ed.), American Mathematical Society, ISBN0821852825
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, ISBN978-0-608-30568-4
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restricted, root, system, mathematics, restricted, root, systems, sometimes, called, relative, root, systems, root, systems, associated, with, symmetric, space, associated, finite, reflection, group, called, restricted, weyl, group, restricted, root, system, s. 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 editSatake diagramReferences editBump 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 nbsp This mathematics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Restricted root system amp oldid 1199305967, wikipedia, wiki, book, books, library,
