FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER-MATRIX

We present a ''natural finitization'' of the fermionic q-series (certa in generalizations of the Rogers-Ramanujan sums) which were recently c onjectured to be equal to Virasoro characters of the unitary minimal c onformal field theory (CFT) M(p, p + 1). Within the quasi-particle int erpretation of the fermionic q-series this finitization amounts to int roducing nn ultraviolet cutoff, which - contrary to a lattice spacing - does not modify the linear dispersion relation. The resulting polyno mials are conjectured (proven, for p = 3,4) to be equal to corner tran sfer matrix (CTM) sums which arise in the computation of order paramet ers in regime III of the r = p + 1 RSOS model of Andrews, Baxter and F orrester. Following Schur's proof of the Rogers-Ramanujan identities, these authors have shown that the infinite lattice limit of the CTM su ms gives what later became known as the Rocha-Caridi formula for the V irasoro characters. Thus we provide a proof of the fermionic q-series representation for the Virasoro characters for p = 4 (the case p = 3 i s 'trivial''), in addition to extending the remarkable connection betw een CFT and off-critical RSOS models. We also discuss finitizations of the CFT modular-invariant partition functions.