Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Jordan Structure of Two Dimensional Loop Models   We show how to use the link representation of the transfer matrix $D_N$ of
loop models on the lattice to calculate partition functions, at criticality, of
the Fortuin-Kasteleyn model with various boundary conditions and parameter
$\beta = 2 \cos(\pi(1-a/b)), a,b\in \mathbb N$ and, more specifically,
partition functions of the corresponding $Q$-Potts spin models, with
$Q=\beta^2$. The braid limit of $D_N$ is shown to be a central element
$F_N(\beta)$ of the Temperley-Lieb algebra $TL_N(\beta)$, its eigenvalues are
determined and, for generic $\beta$, a basis of its eigenvectors is constructed
using the Wenzl-Jones projector. To any element of this basis is associated a
number of defects $d$, $0\le d\le N$, and the basis vectors with the same $d$
span a sector. Because components of these eigenvectors are singular when $b
\in \mathbb{Z}^*$ and $a \in 2 \mathbb{Z} + 1$, the link representations of
$F_N$ and $D_N$ are shown to have Jordan blocks between sectors $d$ and $d'$
when $d-d' < 2b$ and $(d+d')/2 \equiv b-1 \ \textrm{mod} \ 2b$ ($d>d'$). When
$a$ and $b$ do not satisfy the previous constraint, $D_N$ is diagonalizable.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th