Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The su(n) WZNW fusion ring as integrable model: a new algorithm to
  compute fusion coefficients   This is a proceedings article reviewing a recent combinatorial construction
of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one
novel aspect: the explicit derivation of an algorithm for the computation of
fusion coefficients different from the Kac-Walton formula. The discussion is
presented from the point of view of a vertex model in statistical mechanics
whose partition function generates the fusion coefficients. The statistical
model can be shown to be integrable by linking its transfer matrix to a
particular solution of the Yang-Baxter equation. This transfer matrix can be
identified with the generating function of an (infinite) set of polynomials in
a noncommutative alphabet: the generators of the local affine plactic algebra.
The latter is a generalisation of the plactic algebra occurring in the context
of the Robinson-Schensted correspondence. One can define analogues of Schur
polynomials in this noncommutative alphabet which become identical to the
fusion matrices when represented as endomorphisms over the state space of the
integrable model. Crucial is the construction of an eigenbasis, the Bethe
vectors, which are the idempotents of the fusion algebra.

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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg