On Kostant’s theorem for Lie superalgebras

Abstract

We study finite W-algebras for even regular (principal) nilpotent elements for classical Lie superalgebras. We give the precise description of the principal finite W-algebra for the exceptional simple Lie superalgebra D(2,1;α)and obtain partial results for osp(1|2n). We show that the principal finite W-algebra for the Lie superalgebra Q(n)is isomorphic to a factor algebra of the super-Yangian of Q (1).