Weight modules of D(2,1, α)

Let g be a basic Lie superalgebra. A weight module M over g is called finite if all of its weight spaces are finite dimensional, and it is called bounded if there is a uniform bound on the dimension of a weight space. The minimum bound is called the degree of M. For g = D(2,1, α), we prove that every simple weight module M is bounded and has degree less than or equal to 8. This bound is attained by a cuspidal module M if and only if M belongs to a g,g_0¯-coherent family Lλ_Γ^μ for some typical module L (λ). Cuspidal modules which correspond to atypical modules have degree less than or equal to 6 and greater than or equal to 2.