Embedding of bases: From the M(2,2κ+1) to the M(3,4κ+2−δ) models

A new quasi-particle basis of states is presented for all the irreducible modules of the M(3,p) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field ϕ2,1. This leads to a fermionic expression for particular combinations of irreducible M(3,p) characters, which turns out to be identical with the previously known formula. Quite remarkably, this new quasi-particle basis embodies a sort of embedding, at the level of bases, of the minimal models M(2,2κ+1) into the M(3,4κ+2−δ) ones, with 0⩽δ⩽3.