Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formulae of $\imath$-divided powers in ${\mathbf U}_q(\mathfrak{sl}_2)$   The existence of the $\imath$-canonical basis (also known as the
$\imath$-divided powers) for the coideal subalgebra of the quantum
$\mathfrak{sl}_2$ were established by Bao and Wang, with conjectural explicit
formulae. In this paper we prove the conjectured formulae of these
$\imath$-divided powers. This is achieved by first establishing closed formulae
of the $\imath$-divided powers in basis for quantum $\mathfrak{sl}_2$ and then
formulae for the $\imath$-canonical basis in terms of Lusztig's divided powers
in each finite-dimensional simple module of quantum $\mathfrak{sl}_2$. These
formulae exhibit integrality and positivity properties.

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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat