Journal of Lie Theory, Vol. 10, No. 1, pp. 213-220 (2000)

On minimal parabolic subgroups of exponential Lie groups

Dragomir Z. Djokovic

Department of Pure Mathematics
University of Waterloo
Waterloo, Ontario N2L 3G1

Abstract: The conjecture in Problem 6.3 of [4] is refuted by a counterexample: minimal parabolic subgroups may not be used for testing the surjectivity of the exponential function. Specifically, the minimal parabolic subgroups of GL$_n({\Bbb H})$ are not exponential for $n\ge8$. The same is true for Sp$(p,q)$ if $p\ge q\ge8$ and SO$^*(2n)$ if $n\ge15$. However, we show that the minimal parabolic subgroups of SO$(p,1)^\circ$ and of U$(p,q)$ are exponential.}

{\eightrm [4] Hofmann, K. H., and D. Z. \DJ okovic {\eightit Problems on the exponential function of Lie groups} in "Positivity in Lie Theory: Open Problems" (J. Hilgert, J. D. Lawson, K.-H. Neeb, and E. B. Vinberg, Eds.), Walter de Gruyter, Berlin 1998, pp. 45-69

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