Degenerate orbits of adjoint representation of orthogonal and unitary groups regarded as algebraic submanifolds
We suggest a method for describing some types of degenerate orbits of orthogonal and unitary groups in the corresponding Lie algebras as level surfaces of a special collection of polynomial functions. This method allows one to describe orbits of the types SO(2n)/SO(2k)×SO(2) n−k , SO(2n+1)/SO(2k+1)×...
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| Date: | 1997 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5079 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We suggest a method for describing some types of degenerate orbits of orthogonal and unitary groups in the corresponding Lie algebras as level surfaces of a special collection of polynomial functions. This method allows one to describe orbits of the types SO(2n)/SO(2k)×SO(2) n−k , SO(2n+1)/SO(2k+1)×SO(2) n−k , and (S)U(n)/(S)(U(2k)×U(2) n−k ) in so(2n), so(2n+1), and (s)u(n), respectively. In addition, we show that the orbits of minimal dimensions of the groups under consideration can be described in the corresponding algebras as intersections of quadries. In particular, this approach is used for describing the orbit CP n−1⊂u(n). |
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