Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the planar algebra of Ocneanu's asymptotic inclusion   In recent joint work with V. Jones and D. Shlyakhtenko, we have given a
diagrammatic description of Popa's symmetric enveloping inclusion for planar
algebra subfactors. In this paper we give a diagrammatic construction of the
associated Jones tower, in the case that the planar algebra is finite-depth. We
then use this construction to describe the planar algebra of the symmetric
enveloping inclusion, which is known to be isomorphic to the planar algebra of
Ocneanu's asymptotic inclusion by a result of Popa. As an application we give a
planar algebraic computation of the (reduced) fusion algebra of the asymptotic
inclusion, recovering some well-known results of Ocneanu and Evans-Kawahigashi.

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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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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: dg-ga
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con