Surprising properties of centralisers in classical Lie algebras

Details Surprising properties of centralisers in classical Lie algebras Surprising properties of centralisers in classical Lie algebras

2008-03-03

arxiv.org/abs/0803.0285v2

Mathematics

Representation Theory

Final version, to appear in Ann. Inst. Fourier (Grenoble), v. 59 (2009)

Scientific paper

Let $g$ be a classical Lie algebra, i.e., either $gl_n$, $sp_n$, or $so_n$ and let $e\in g$ be a nilpotent element. We study various properties of centralisers $g_e$. The first four sections deal with rather elementary questions, like the centre of $g_e$, commuting varieties associated with $g_e$, or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on $g_e^*$ and symmetric invariants of $g_e$.

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