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arXiv · 2204.01051

Formulae of $\imath$-divided powers in ${\bf U}_q(\mathfrak{sl}_2)$, III

Xinhong Chen·Weiqiang Wang
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Abstract

The $\imath$-divided powers (depending on a parity) form the $\imath$canonical basis for the split rank 1 $\imath$quantum group and they are a basic ingredient for $\imath$quantum groups of higher rank. We obtain closed formulae for the structure constants for multiplication of the $\imath$-divided powers. Closed formulae for the comultiplication of the $\imath$-divided powers are also obtained. These structure constants are integral and positive.

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BibTeXRIS

Xinhong Chen, Weiqiang Wang. 2022-04-03. Formulae of $\imath$-divided powers in ${\bf U}_q(\mathfrak{sl}_2)$, III. https://arxiv.org/abs/2204.01051

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