Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simply-laced root systems arising from quantum affine algebras   Let $U_q'(\mathfrak{g})$ be a quantum affine algebra with an indeterminate
$q$ and let $\mathscr{C}_{\mathfrak{g}}$ be the category of finite-dimensional
integrable $U_q'(\mathfrak{g})$-modules. We write
$\mathscr{C}_{\mathfrak{g}}^0$ for the monoidal subcategory of
$\mathscr{C}_{\mathfrak{g}}$ introduced by Hernandez-Leclerc. In this paper, we
associate a simply-laced finite type root system to each quantum affine algebra
$U_q'(\mathfrak{g})$ in a natural way, and show that the block decompositions
of $\mathscr{C}_{\mathfrak{g}}$ and $\mathscr{C}_{\mathfrak{g}}^0$ are
parameterized by the lattices associated with the root system. We first define
a certain abelian group $\mathcal{W}$ (resp. $\mathcal{W}_0$) arising from
simple modules of $ \mathscr{C}_{\mathfrak{g}}$ (resp.
$\mathscr{C}_{\mathfrak{g}}^0$) by using the invariant $\Lambda^\infty$
introduced in the previous work by the authors. The groups $\mathcal{W}$ and
$\mathcal{W}_0$ have the subsets $\Delta$ and $\Delta_0$ determined by the
fundamental representations in $ \mathscr{C}_{\mathfrak{g}}$ and
$\mathscr{C}_{\mathfrak{g}}^0$ respectively. We prove that the pair $(
\mathbb{R} \otimes_\mathbb{Z} \mathcal{W}_0, \Delta_0)$ is an irreducible
simply-laced root system of finite type and the pair $( \mathbb{R}
\otimes_\mathbb{Z} \mathcal{W}, \Delta) $ is isomorphic to the direct sum of
infinite copies of $( \mathbb{R} \otimes_\mathbb{Z} \mathcal{W}_0, \Delta_0)$
as a root system.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph