Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Combinatorial Approach to Root Multiplicities of a Special Type Rank 3
  Kac-Moody Algebras   In this paper, we calculate the dimension of root spaces
$\mathfrak{g}_{\lambda}$ of a special type rank $3$ Kac-Moody algebras
$\mathfrak{g}$. We first introduce a special type of elements in
$\mathfrak{g}$, which we call elements in standard form. Then, we prove that
any root space is spanned by these elements. By calculating the number of
linearly independent elements in standard form, we obtain a formula for the
dimension of root spaces $\mathfrak{g}_{\lambda}$, which depends on the root
$\lambda$.

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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph