Surprising properties of centralisers in classical Lie algebras

2008/03/03 by Oksana Yakimova, Yakimova, Oksana
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0803.0285

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

arxiv created 2008/11/24 · arxiv updated 2009/12/01

Abstract

Let g be a classical Lie algebra, i.e., either gl_n, sp_n, or so_n and let e∈ 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.

Related

• Centralisers in Classical Lie Algebras
• The centralisers of nilpotent elements in classical Lie algebras
• On the derived algebra of a centraliser
• The index of a Lie algebra, the centraliser of a nilpotent element, and the normaliser of the centraliser
• On symmetric invariants of centralisers in reductive Lie algebras