On Kostant's theorem for the Lie superalgebra Q(n)

In this paper we study finite W  -algebras for basic superalgebras and Q(n)Q(n) associated with the regular even nilpotent coadjoint orbits. We prove that this algebra satisfies the Amitsur–Levitzki identity and therefore all its irreducible representations are finite-dimensional. In the case of Q(n)Q(n) we give an explicit description of the W  -algebra in terms of generators and relations and realize it as a quotient of the super-Yangian of Q(1)Q(1).