Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple bijection between standard (n,n,n) tableaux and irreducible
  webs for sl_3   Combinatorial spiders are a model for the invariant space of the tensor
product of representations. The basic objects, webs, are certain directed
planar graphs with boundary; algebraic operations on representations correspond
to graph-theoretic operations on webs. Kuperberg developed spiders for rank 2
Lie algebras and sl_2. Building on a result of Kuperberg's, Khovanov-Kuperberg
found a recursive algorithm giving a bijection between standard Young tableaux
of shape (n,n,n) and irreducible webs for sl_3 whose boundary vertices are all
sources. In this paper, we give a simple and explicit map from standard Young
tableaux of shape (n,n,n) to irreducible webs for sl_3 whose boundary vertices
are all sources, and show that it is the same as Khovanov-Kuperberg's map. Our
construction generalizes to some webs with both sources and sinks on the
boundary. Moreover, it allows us to extend the correspondence between webs and
tableaux in two ways. First, we provide a short, geometric proof of
Petersen-Pylyavskyy-Rhoades's recent result that rotation of webs corresponds
to jeu-de-taquin promotion on (n,n,n) tableaux. Second, we define another
natural operation on tableaux called a shuffle, and show that it corresponds to
the join of two webs. Our main tool is an intermediary object between tableaux
and webs that we call an m-diagram. The construction of m-diagrams, like many
of our results, applies to shapes of tableaux other than (n,n,n).

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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex