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Invariant analytic hypersurfaces in complex Lie groups

Published online by Cambridge University Press:  17 April 2009

Bruce Gilligan
Bruce Gilligan
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Canada S4S 0A2, e-mail: [email protected]
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Suppose G is a complex Lie group and H is a closed complex subgroup of G. Let G′ denote the commutator subgroup of G. If there are no nonconstant holomorphic functions on G/H and H is not contained in any proper parabolic subgroup of G, then Akhiezer [2] asked whether every analytic hypersurface in G which is invariant under the right action of H is also invariant under the right action of G′. In this paper we answer a related question in two settings. Under the assumptions stated above we show that the orbits of the radical of G in G/H cannot be Cousin groups, provided G/H is Kähler. We also introduce an intermediate fibration of G/H induced by the holomorphic reduction of the radical orbits and resolve the related question in a situation arising from this fibration.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 343 - 349
Copyright
Copyright © Australian Mathematical Society 2004

References

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