×

Satake diagrams and restricted root systems of semisimple pseudo-Riemannian symmetric spaces. (English) Zbl 1191.53033

The paper completes the list of Satake diagrams and restricted root systems for classical semisimple pseudo-Riemannian symmetric spaces, including signatures of roots. A similar work is planned for the exceptional types.

MSC:

53C35 Differential geometry of symmetric spaces
17B20 Simple, semisimple, reductive (super)algebras
17B22 Root systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. Berger, Les espaces symétriques noncompacts, Ann. Sci. École Norm. Sup., 74 (1957), 85-177. · Zbl 0093.35602
[2] S. Helgason, Differential geometry, Lie groups, and symmetric spaces , Graduate Studies in Mathematics, vol. 34, American Mathematical Society, 2001. · Zbl 0993.53002
[3] K. Kondo, Local orbit types of \(S\)-representations of symmetric \(\mathbf R\)-spaces, Tokyo J. Math., 26 (2003), 67-81. · Zbl 1050.53034 · doi:10.3836/tjm/1244208683
[4] O. Loos, Symmetric spaces. II: Compact spaces and classification, W. A. Benjamin, Inc., New York-Amsterdam, 1969. · Zbl 0175.48601
[5] T. Oshima and J. Sekiguchi, The restricted root system of a semisimple symmetric pair, Adv. Stud. Pure Math., 4 (1984), 433-497. · Zbl 0577.17004
[6] W. Rossmann, The structure of semisimple symmetric spaces, Canad. J. Math., 31 (1979), 157-180. · Zbl 0357.53033 · doi:10.4153/CJM-1979-017-6
[7] H. Tamaru, The local orbit types of symmetric spaces under the actions of the isotropy subgroups, Differential Geom. Appl., 11 (1999), 29-38. · Zbl 0941.53035 · doi:10.1016/S0926-2245(99)00023-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.