Young supertableaux and the large N=4 superconformal algebra

In this paper we consider unitary highest weight irreducible representations of the 'Large' N = 4 superconformal algebra A(gamma) in the Ramond sector as infinite-dimensional graded modules of its zero mode subalgebra, su(2 vertical bar 2). We describe how representations of su(2 vertical bar 2) may be classified using Young supertableaux, and use the decomposition of A(gamma) as an su(2 vertical bar 2) module to discuss the states which contribute to the supersymmetric index I-1, previously proposed in the literature by Gukov, Martinec, Moore and Strominger.