Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual Perfect Bases and dual perfect graphs   We introduce the notion of dual perfect bases and dual perfect graphs. We
show that every integrable highest weight module $V_q(\lambda)$ over a quantum
generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and
its dual perfect graph is isomorphic to the crystal $B(\lambda)$. We also show
that the negative half $U_{q}^{-}(\mathcal{g})$ has a dual perfect basis whose
dual perfect graph is isomorphic to the crystal $B(\infty)$. More generally, we
prove that all the dual perfect graphs of a given dual perfect space are
isomorphic as abstract crystals. Finally, we show that the isomorphism classes
of finitely generated graded projective indecomposable modules over a
Khovanov-Lauda-Rouquier algebra and its cyclotomic quotients form dual perfect
bases for their Grothendieck groups.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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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: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex