Centers of centralizers of nilpotent elements in Lie superalgebras sl(m | n) or osp(m | 2n)

Let G be the simple algebraic supergroup SL(m vertical bar n) or osp(m vertical bar 2n) over C. Let g = Lie((G) over bar) = g (0) over bar circle plus g (1) over bar and let G = (G) over bar (C), where C is considered as a superalgebra concentrated in even degree. Suppose e is an element of g (0) over bar is nilpotent. We describe the centralizer g(e) of e in g and its center z(g(e)). In particular, we give bases for g(e), z(g(e)) and (z(g(e)))(Ge). We also determine the labeled Dynkin diagram Delta with respect to a and subsequently describe the relation between (z(g(e)))G(e) and Delta.