Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-05
Lett.Math.Phys. 37 (1996) 49-66
Physics
High Energy Physics
High Energy Physics - Theory
Several references, one further explicit result and several discussion remarks added
Scientific paper
10.1007/BF00400138
We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ 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 truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ 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.
Berkovich Alexander
McCoy Barry M.
No associations
LandOfFree
Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-676432