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- W2809927390 abstract "We consider the positive part $U^+_q$ of the quantized enveloping algebra $U_q(widehat{mathfrak{sl}}_2)$. The algebra $U^+_q$ has a presentation involving two generators and two relations, called the $q$-Serre relations. There is a PBW basis for $U^+_q$ due to Damiani, and a PBW basis for $U^+_q$ due to Beck. In 2019 we used Catalan words and a $q$-shuffle algebra to express the Damiani PBW basis in closed form. In this paper we use a similar approach to express the Beck PBW basis in closed form. We also consider how the Damiani PBW basis and the Beck PBW basis are related to the alternating PBW basis for $U^+_q$." @default.
- W2809927390 created "2018-07-10" @default.
- W2809927390 creator A5059249005 @default.
- W2809927390 date "2021-08-28" @default.
- W2809927390 modified "2023-09-27" @default.
- W2809927390 title "Using Catalan words and a $q$-shuffle algebra to describe the Beck PBW basis for the positive part of $U_q(widehat{mathfrak{sl}}_2)$" @default.
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