A uniform approach to the Damiani, Beck, and alternating PBW bases for the positive part of Uq(𝔰𝔩 2)

This paper is about the positive part [Formula: see text] of the [Formula: see text]-deformed enveloping algebra [Formula: see text]. The literature contains at least three PBW bases for [Formula: see text], called the Damiani, the Beck, and the alternating PBW bases. These PBW bases are related via exponential formulas. In this paper, we introduce an exponential generating function whose argument is a power series involving the Beck PBW basis and an integer parameter [Formula: see text]. The cases [Formula: see text] and [Formula: see text] yield the known exponential formulas for the Damiani and alternating PBW bases, respectively. The case [Formula: see text] appears in the author’s previous paper. In this paper, we give a comprehensive study of the generating function for an arbitrary integer [Formula: see text]. In our main result, we express the coefficients of the generating function in closed form.