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BIMSA 可积系统讨论班
BIMSA 可积系统讨论班
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 $U_q(\hat{\mathfrak{sl}}_2)$
演讲者
时间
2023年12月22日 13:30 至 15:00
地点
A6-101
摘要
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.
演讲者介绍
Chenwei Ruan completed his Ph.D. at the University of Wisconsin-Madison in 2024 under Paul Terwilliger. He is currently a Chern Instructor at the Beijing Institute of Mathematical Sciences and Applications. His research focuses on quantum algebras and representation theory, investigating the combinatorial structures underlying integrable systems. His recent work examines special bases and generating functions in quantum group theory, bridging abstract algebra with applications in mathematical physics.