Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Temperley-Lieb K-matrices   This work concerns to the studies of boundary integrability of the vertex
models from representations of the Temperley-Lieb algebra associated with the
quantum group ${\cal U}_{q}[X_{n}]$ for the affine Lie algebras
  $X_{n}$ = $A_{1}^{(1)}$, $B_{n}^{(1)}$, $C_{n}^{(1)}$ and $D_{n}^{(1)}$.
  A systematic computation method is used to constructed solutions of the
boundary Yang-Baxter equations. We find a $2n^{2}+1$ free parameter solution
for $A_{1}^{(1)} $ spin-$(n-1/2)$ and $ C_{n}^{(1)}$ vertex models. It turns
that for $A_{1}^{(1)} $ spin-$n$, $ B_{n}^{(1)}$ and $D_{n}^{(1)}$ vertex
models, the solution has $2n^{2}+2n+1$ free parameters.

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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: cs