Note on prehomogeneous vector spaces |
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| Authors: | Janez Bernik Mitja Mastnak |
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| Institution: | 1. Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
2. Department of Mathematics and Computer Science, Saint Mary’s University, Halifax, NS, B3H 3C3, Canada
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| 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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