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The positive part of $U_q \left( \widehat{\mathfrak{sl}_2} \right)$ and its embedding into a q-shuffle algebra
The positive part of $U_q \left( \widehat{\mathfrak{sl}_2} \right)$ and its embedding into a q-shuffle algebra
组织者
演讲者
时间
2024年10月18日 10:00 至 11:30
地点
A3-4-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
The q-deformed enveloping algebra $U_q \left( \widehat{\mathfrak{sl}_2} \right)$ and its positive part $U_q^+$ are studied in both mathematics and mathematical physics. ln 1995 , Rosso obtained an embedding of the algebra $U_q^+$ into a q-shuffle algebra. In the literature, there are three PBW bases for $U_q^+$ due to Damiani, Beck, Terwilliger respectively. The Damiani and the Beck PBW bases were originally defined using recurrence relations. Later, Terwilliger used the Rosso embedding to obtain closed forms for these two bases. Terwilliger also obtained the alternating PBW basis for $U_q^+$ using the Rosso embedding. The three PBW bases are related via exponential formulas. ln recent years, I used the Rosso embedding to obtain a uniform approach to the PBW bases and the exponential forrnulas aforementioned. I also studied sonme elements of interest related to the alternating PBW basis. We will discuss these results in this talk.
This talk is based on arXiv:2305.11152, arXiv:2408.02633
This talk is based on arXiv:2305.11152, arXiv:2408.02633