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BIMSA Integrable Systems Seminar
A uniform approach to the Damiani, Beck, and alternating PBW bases for the positive part of $U_q(\hat{\mathfrak{sl}}_2)$
A uniform approach to the Damiani, Beck, and alternating PBW bases for the positive part of $U_q(\hat{\mathfrak{sl}}_2)$
Organizers
Speaker
Time
Friday, December 22, 2023 1:30 PM - 3:00 PM
Venue
A6-101
Abstract
The q-deformed enveloping algebra $U_q(\hat{\mathfrak{sl}}_2)$ and its positive part $U_q^+$ are studied in both mathematics and mathematical physics. The literature contains at least three PBW bases for $U_q^+$, called the Damiani, the Beck, and the alternating PBW bases. These PBW bases are related via exponential formulas. In this talk, we will introduce an exponential generating function whose argument is a power series involving the Beck PBW basis and an integer parameter m. The cases m = 2 and m = −1 yield the known exponential formulas for the Damiani and alternating PBW bases, respectively. We will present two results on the generating function for an arbitrary integer m. The first result gives a factorization of the generating function. In the second result, we express the coefficients of the generating function in closed form.