Cartan-decomposition subgroups of $\operatorname {SO}(2,n)$
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- by Hee Oh and Dave Witte Morris PDF
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Abstract:
For $G = \operatorname {SL} (3,\mathbb {R})$ 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 $G$.References
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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
- MR Author ID: 615083
- 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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 1-38
- MSC (2000): Primary 22E46; Secondary 20G20, 22E15, 57S20
- DOI: https://doi.org/10.1090/S0002-9947-03-03428-7
- MathSciNet review: 2020022