Sets of rigged paths with Virasoro characters

Abstract Let {Mr,s(p,p′)}1≤r≤p−1,1≤s≤p′−1 be the irreducible Virasoro modules in the (p,p′)-minimal series. In our previous paper, we have constructed a monomial basis of ⊕r=1p−1Mr,s(p,p′) in the case 1<p′/p<2. By ‘monomials’ we mean vectors of the form $\phi^{(r_{L},r_{L-1})}_{-n_{L}}\cdots\phi^{(r_{1},r_{0})}_{-n_{1}}{|r_{0},s\rangle }$ , where φ−n(r′,r):Mr,s(p,p′)→Mr′,s(p,p′) are the Fourier components of the (2,1)-primary field and |r0,s〉 is the highest weight vector of $M^{(p,p')}_{r_{0},s}$ . In this article, we introduce for all p<p′ with p≥3 and s=1 a subset of such monomials as a conjectural basis of ⊕r=1p−1Mr,1(p,p′). We prove that the character of the combinatorial set labeling these monomials coincides with the character of the corresponding Virasoro module. We also verify the conjecture in the case p=3.