A solution to two party typicality using representation theory of the symmetric group

We show that, given a state on a bipartite system AB, the product of the tensor product of the typical projections for the marginal states on A and B and the typical projection for AB can be used to describe the correct asymptotics of the bipartite state itself, its square, marginals and sqares of the marginals. Typicality is defined using the representation theory of the symmetric group. This result has already been proven, but with a different notion of typicality.