seminar: The symmetric invariants of centralizers and Slodowy grading - Seminar of the session "Vertex algebras, W-algebras, and applications" (continuation 2015)
speaker: Anne Moreau (Université de Poitiers)abstract: Let g be a complex finite-dimensional simple Lie algebra, and let e be a nilpotent element of g. An interesting question, raised by Premet, is whether the algebra of symmetric invariants of the centralizer of e is polynomial. In 2007, Premet, Panyushev and Yamimova resolved the question in some special cases; in particular, the answer is positive for g of type A or C.
In this talk, I will present a joint work with Jean-Yves Charbonnel in which we continue the works of Premet et al. Our main result says that if for some homogeneous generators of S(g)g , the initial homogeneous components of their restrictions the to Slodowy slice of e are algebraically independent, then e satisfies the polynomiality condition. The key to the proof is the use of the Slowody grading induced from the finite W-algebra associated with (g,e).
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