Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crystal Graphs and $q$-Analogues of Weight Multiplicities for the Root
  System $A_n$   We give an expression of the $q$-analogues of the multiplicities of weights
in irreducible $\sl_{n+1}$-modules in terms of the geometry of the crystal
graph attached to the corresponding $U_q(\sl_{n+1})$-modules. As an
application, we describe multivariate polynomial analogues of the
multiplicities of the zero weight, refining Kostant's generalized exponents.

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The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph