Andrews-Gordon type identities from combinations of Virasoro characters

For p ∈ {3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ _1,s ^p,p′ +q ^Δ χ _p-1,s ^p,p′ of Virasoro (W ₂) characters for various values of s, and particular choices of Δ. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews-Gordon identities. For p=3, these identities were conjectured by Bytsko. For p=4, we obtain identities whose form is a variation on that of the p=3 cases. These identities appear to be new. The case (p,p′)=(3,14) is particularly interesting because it relates not only to W ₂, but also to W ₃ characters, and offers W ₃ analogues of the original Andrews-Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al. which involve Gaussian polynomials.