Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic

Let g=g0¯⊕g1¯ be a basic classical Lie superalgebra over an algebraically closed field K whose characteristic p>0 is a good prime for g. Let G0¯ be the reductive algebraic group over K such that Lie(G0¯)=g0¯. Suppose e∈g0¯ is nilpotent. Write ge for the centralizer of e in g and z(ge) for the centre of ge. We calculate a basis for ge and z(ge) by using associated cocharacters τ:K×→G0¯ of e. In addition, we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property for exceptional Lie superalgebras D(2,1;α), G(3) and F(4).