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Rogers–Schur–Ramanujan Type Identities for the
M
(
p
,
p
′) Minimal Models of Conformal Field Theory
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Rogers–Schur–Ramanujan Type Identities for the M( p, p′) Minimal Models of Conformal Field Theory
Alexander Berkovich1, Barry M. McCoy2 and Anne Schilling2
| (1) |
Physikalisches Institut der Rheinischen Friedrich-Wilhelms Universität Bonn, Nussallee 12, D-53115 Bonn, Germany. E-mail:
berkov_a@math.psu.edu, DE |
| (2) |
Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794-3840, USA.¶E-mail: mccoy@max.physics.sunysb.edu;
anne@insti.physics.sunysb.edu, US |
Abstract: 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
for many classes of r and s.
Received: 23 July 1996 / Accepted: 15 May 1997
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