lambda-operations in beta-rings

A beta-ring is supplied with operations beta_H where H runs over the conjugacy classes of subgroups of the symmetric group S_n. In an earlier paper we introduced a second set of operations lambda_H and we show here that the two sets are related by the isomorphism beta_H(-X) = (-1)^n lambda_H(X). We then consider the operations beta_H and lambda_H as combinatorial species, in the sense of Joyal, and express their molecular decomposition as a finite sum of products of the exponential species of degree at most n. We give combinatorial interpretations for beta_{S_n}-structures and lambda_{S_n}-structures and derive various species isomorphisms.