Note on generating functions and connected correlators of 1/2-BPS Wilson loops in N = 4 SYM theory

The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group U(N) are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the representation theory of the symmetric group. This provides a proof of a recent observation by Okuyama. As a by-product, we present a new calculation of the connected 2-point correlator of multiplywound Wilson loops at leading order in 1/N.