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Surprising properties of centralisers in classical Lie algebras

Surprising properties of centralisers in classical Lie algebras

Let ๐”ค be a classical Lie algebra, i.e., either ๐”ค๐”ฉ n , ๐”ฐ๐”ญ n , or ๐”ฐ๐”ฌ n and let e be a nilpotent element of ๐”ค. We study various properties of the centralisers ๐”ค e . The first four sections deal with rather elementary questions, like the centre of โ€ฆ