Continued fractions and fermionic representations for characters ofM(p,p′)minimal models
✍ Scribed by Alexander Berkovich; Barry M. McCoy
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 757 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0377-9017
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✦ Synopsis
We present fermionic sum representations of the characters X~,g of the minimal M (p, p') models for all relatively prime integers p' > p for some allowed values of r and s. Our starting point is binomial (q-binomial) identities derived from a tnmcation of the state counting equations of the X X Z spin 89 chain of anisotropy -A = -cosQr(p/p')). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {if/p} (and p/if), where {x} stands for the fractional part of z. These values are, in fact, the dimensions of the Hermitian irreducible representations of SUq_ (2) (and SUq+ (2)) with q_ = exp(irr{p/p}) (and q+ = exp(iTr(p/p'))). We also establish the duality relation M(p,p') ++ M(p' -p,p') and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.