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Formulae of imath-divided powers in {bf U}_q(mathfrak{sl}₂), III
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Formulae of imath-divided powers in {bf U}_q(mathfrak{sl}₂), III
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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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