Weight modules of D(2,1,a)

Abstract: A weight module of a basic Lie superalgebra 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 the module. For the basic Lie superalgebra D(2,1,a), we prove that every simple weight module is bounded and has degree less than or equal to 8. This bound is attained by a cuspidal module if and only if it is "typical". Atypical cuspidal modules have degree less than or equal to 6 and greater than or equal to 2.