Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion
  Rules   The $sl(2)$ minimal theories are labelled by a Lie algebra pair $(A,G)$ where
$G$ is of $A$-$D$-$E$ type. For these theories on a cylinder we conjecture a
complete set of conformal boundary conditions labelled by the nodes of the
tensor product graph $A\otimes G$. The cylinder partition functions are given
by fusion rules arising from the graph fusion algebra of $A\otimes G$. We
further conjecture that, for each conformal boundary condition, an integrable
boundary condition exists as a solution of the boundary Yang-Baxter equation
for the associated lattice model. The theory is illustrated using the
$(A_4,D_4)$ or 3-state Potts model.

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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an