Wolf space coset spectrum in the large

After reviewing the four eigenvalues (the conformal dimension, two SU(2) quantum number, and U(1) charge) in the minimal (and higher) representations in the Wolf space coset where the N = 4 superconformal algebra is realized by 11 currents in nonlinear way, these four eigenvalues in the higher representations up to two boxes (of Young tableaux) are examined in detail. The eigenvalues associated with the higher spin-1, 2, 3 currents in the (minimal and) higher representations up to two boxes are studied. They are expressed in terms of the two finite parameters (N, k) where the Wolf space coset contains the group SU(N + 2) and the affine KacMoody spin 1 current has the level k. Under the large (N, k) t Hooft-like limit, they are simply linear combinations of the eigenvalues in the minimal representations. As a by product, the three-point functions of the higher spin currents with two scalar operators can be determined at finite (N, k).