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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cartan-decomposition subgroups of $\operatorname{SO}(2,n)$


Authors: Hee Oh and Dave Witte Morris
Journal: Trans. Amer. Math. Soc. 356 (2004), 1-38
MSC (2000): Primary 22E46; Secondary 20G20, 22E15, 57S20
Published electronically: August 25, 2003
MathSciNet review: 2020022
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Abstract | References | Similar Articles | Additional Information

Abstract: For $G = \operatorname{SL} (3,\mathord{\mathbb{R} })$ and $G = \operatorname{SO}(2,n)$, we give explicit, practical conditions that determine whether or not a closed, connected subgroup $H$of $G$ has the property that there exists a compact subset $C$ of $G$with $CHC = G$. To do this, we fix a Cartan decomposition $G = K A^+ K$of $G$, and then carry out an approximate calculation of $(KHK) \cap A^+$for each closed, connected subgroup $H$ of $G$.


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Additional Information

Hee Oh
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: heeoh@math.princeton.edu

Dave Witte Morris
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4
Email: dwitte@math.okstate.edu, dmorris@cs.uleth.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03428-7
PII: S 0002-9947(03)03428-7
Received by editor(s): February 4, 1999
Received by editor(s) in revised form: March 4, 1999, and November 6, 1999
Published electronically: August 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society