Abstract
Let \(V\) be a complex prehomogeneous vector space under the action of a linear algebraic group \(G\). Assume the poset of orbit closures in the Zariski topology \(\{\overline{Gx}:x\in V\}\) coincides with a (partial) flag \(V_0=0<V_1<\dots <V_k=V\) in \(V\). Then for any Borel subgroup \(B\) of \(G\), the poset \(\{\overline{B x}:x\in V\}\) coincides with a full flag in \(V\).
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Communicated by J. S. Wilson.
J. Bernik was supported in part by Research and Development Agency of Slovenia. M. Mastnak was supported by NSERC of Canada.
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Bernik, J., Mastnak, M. Note on prehomogeneous vector spaces. Monatsh Math 174, 371–376 (2014). https://doi.org/10.1007/s00605-013-0523-0
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DOI: https://doi.org/10.1007/s00605-013-0523-0