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

Abstract

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

21 pages, v2, results upgraded to general parameters, accepted for publication