Journal of Lie Theory, Vol. 11, No. 2, pp. 505-543 (2001)

Cartan-Decomposition Subgroups of SU(2,n)

Alessandra Iozzi and Dave Witte

Department of Mathematics
University of Maryland
College Park, MD 20910 USA
Current address:
ETH Zentrum
CH-8092 Zürich Switzerland
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078 USA

Abstract: We give explicit, practical conditions that determine whether or not a closed, connected subgroup $H$ of $G = SU(2,n)$ 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 $G$. This generalizes the work of H. Oh and D. Witte for $G = SO(2,n)$.

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