Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical bases of $q$-Brauer algebras and $\imath$Schur dualities   Expanding the classical work of Kazhdan-Lusztig, we construct a bar
involution and canonical bases on the $q$-Brauer algebra introduced by Wenzl.
We define explicit actions of the $q$-Brauer algebra on the tensor spaces, and
formulate $\imath$Schur dualities between the $q$-Brauer algebra and the
$\imath$quantum groups of type AI and AII respectively.

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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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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: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom