PBW bases of irreducible Ising modules

Abstract

To every h+N-graded module M over an N-graded conformal vertex algebra V, we associate an increasing filtration (GpM)p∈Z, which is compatible with the filtrations introduced by Haisheng Li. The associated graded vector space grG(M) is naturally a module over the vertex Poisson algebra grG(V). We study grG(M) for the three irreducible modules over the Ising model Vir3,4, namely Vir3,4=L(1/2,0), L(1/2,1/2) and L(1/2,1/16). We obtain an explicit PBW basis of each of these modules and a formula for their refined characters, which are related to Nahm sums for the matrix (8332).