Proceedings of the Japan Academy, Series A, Mathematical Sciences

Proper actions of $SL(2,\mathbf{R})$ on semisimple symmetric spaces

Takayuki Okuda

Full-text: Open access

Abstract

We classify semisimple symmetric spaces $G/H$ for which there exist proper $SL(2,\mathbf{R})$-actions via $G$. This leads us to the classification of semisimple symmetric spaces that admit surface groups as discontinuous groups.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 3 (2011), 35-39.

Dates
First available in Project Euclid: 3 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1299161393

Digital Object Identifier
doi:10.3792/pjaa.87.35

Mathematical Reviews number (MathSciNet)
MR2802605

Zentralblatt MATH identifier
1221.22020

Subjects
Primary: 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C35: Symmetric spaces [See also 32M15, 57T15] 57S30: Discontinuous groups of transformations

Keywords
Proper action symmetric space surface group nilpotent orbit weighted Dynkin diagram Satake diagram

Citation

Okuda, Takayuki. Proper actions of $SL(2,\mathbf{R})$ on semisimple symmetric spaces. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 3, 35--39. doi:10.3792/pjaa.87.35. https://projecteuclid.org/euclid.pja/1299161393


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