FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER-MATRIX

We present a ''natural finitization'' of the fermionic q-series (certain generalizations of the Rogers-Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary minimal conformal field theory (CFT) M(p, p + 1). Within the quasi-particle interpretation of the fermionic q-series this finitization amounts to introducing nn ultraviolet cutoff, which - contrary to a lattice spacing - does not modify the linear dispersion relation. The resulting polynomials are conjectured (proven, for p = 3,4) to be equal to corner transfer matrix (CTM) sums which arise in the computation of order parameters in regime III of the r = p + 1 RSOS model of Andrews, Baxter and Forrester. Following Schur's proof of the Rogers-Ramanujan identities, these authors have shown that the infinite lattice limit of the CTM sums gives what later became known as the Rocha-Caridi formula for the Virasoro characters. Thus we provide a proof of the fermionic q-series representation for the Virasoro characters for p = 4 (the case p = 3 is 'trivial''), in addition to extending the remarkable connection between CFT and off-critical RSOS models. We also discuss finitizations of the CFT modular-invariant partition functions.