In this paper we give a detailed proof of the classification of extremal (=massless) unitary highest weight representations in the Neveu Schwarz and Ramond sectors of the big N=4 superconformal algebra which can be found in 5. Our results agree with the general conjectures about classification of unitary highest weight representation of minimal W-algebras attached to basic Lie superalgebras formulated in 10, 11, and complete their proof for the big N=4 superconformal algebra.
Kač et al. (Mon,) studied this question.