Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of Irreducible Representations over Khovanov-Lauda-Rouquier
  Algebras of Finite Classical Type   We give an explicit construction of irreducible modules over
Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients
$R^{\lambda}$ for finite classical types using a crystal basis theoretic
approach. More precisely, for each element $v$ of the crystal $B(\infty)$
(resp. $B(\lambda)$), we first construct certain modules $\nabla(\mathbf{a};k)$
labeled by the adapted string $\mathbf{a}$ of $v$. We then prove that the head
of the induced module $\ind \big(\nabla(\mathbf{a};1) \boxtimes...\boxtimes
\nabla(\mathbf{a};n)\big)$ is irreducible and that every irreducible $R$-module
(resp. $R^{\lambda}$-module) can be realized as the irreducible head of one of
the induced modules $\ind (\nabla(\mathbf{a};1) \boxtimes...\boxtimes
\nabla(\mathbf{a};n))$. Moreover, we show that our construction is compatible
with the crystal structure on $B(\infty)$ (resp. $B(\lambda)$).

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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas