Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braid group action and quasi-split affine $\imath$quantum groups I   This is the first of two papers on quasi-split affine quantum symmetric pairs
$\big(\widetilde{\mathbf U}(\widehat{\mathfrak g}), \widetilde{{\mathbf
U}}^\imath \big)$, focusing on the real rank one case, i.e., $\mathfrak{g}=
\mathfrak{sl}_3$ equipped with a diagram involution. We construct explicitly a
relative braid group action of type $A_2^{(2)}$ on the affine $\imath$quantum
group $\widetilde{{\mathbf U}}^\imath$. Real and imaginary root vectors for
$\widetilde{{\mathbf U}}^\imath$ are constructed, and a Drinfeld type
presentation of $\widetilde{{\mathbf U}}^\imath$ is then established. This
provides a new basic ingredient for the Drinfeld type presentation of higher
rank quasi-split affine $\imath$quantum groups in the sequel.

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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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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: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci