Rogers-Schur-Ramanujan type identities for the $M(p,p')$ minimal models of conformal field theory

Details Rogers-Schur-Ramanujan type identities for the $M(p,p')$ minimal models of conformal field theory Rogers-Schur-Ramanujan type identities for the $M(p,p')$ minimal models of conformal field theory

1996-07-15

arxiv.org/abs/q-alg/9607020v2

Commun.Math.Phys. 191 (1998) 325-395

Physics

High Energy Physics

High Energy Physics - Theory

85 pages in harvmac with 16 figures. Stylistic revisions particularly in section 8 and appendix B and an additional proof adde

Scientific paper

10.1007/s002200050271

We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model $M(p,p').$ The proof uses the continued fraction decomposition of $p'/p$ introduced by Takahashi and Suzuki for the study of the Bethe's Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of the fermionic form of the characters which satisfy the same recursion relations as the bosonic polynomials of Forrester and Baxter. We use this method to get fermionic representations of the characters $\chi_{r,s}^{(p,p')}$ for many classes of $r$ and $s.$

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