Symmetric invariants of centralisers in semisimple Lie algebras

Alexander Premet, University of Manchester, England

Let e be a nilpotent element in a finite dimensional complex simple Lie algebra g and denote by ge the centralizer of e in g. In my talk, based on recent joint work with Panyushev and Yakimova, I am going to present some results on the algebra A(e):=S(ge)ge of symmetric invariants of ge. It turns out that in many cases A(e) is a graded polynomial algebra in l=rk(g) variables. For example, this holds for all nilpotent elements in g=gl(n) and g=sp(2n).

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