q-Virasoro/W algebra at root of unity and parafermions

Abstract

We demonstrate that the parafermions appear in the r-th root of unity limit of q-Virasoro/Wn algebra. The proper value of the central charge of the coset model slˆ(n)r⊕slˆ(n)m−nslˆ(n)m−n+r is given from the parafermion construction of the block in the limit.