学术报告 报告题目1：Quantum queer supergroups and Berezinians
报 告 人：黎允楠 博士（广州大学）
报告时间：2017年11月11日 （星期六）上午10：00-11：00
报告题目2：Representation of affine Lie superalgebra and superanalogy EALA
报 告 人：汪永杰 博士（台湾大学）
报告时间：2017年11月11日 （星期六）上午11：00-12：00
邀 请 人：常智华 博士
报告地点：四号楼4318
欢迎广大师生前往！
数学学院
2017年11月10日
报告1摘要：In this talk, we first introduce the quantum coordinate superalgebra $A_q(n)$ of type $Q$, derived from the quantized universal enveloping superalgebra of queer Lie superalgebra. Then referring to Manin's approach to the quantum general linear supergroup, we consider the extension problem from this $A_q(n)$ to a Hopf superalgebra, so-called the quantum queer supergroup. In particular, we confirm the existence of a special grouplike element in such Hopf superalgebra, called the quantum queer Berezinian, as the queer super analogue of quantum determinant. Some questions unsolved will also be raised for further study. This is a joint work with Jiao Zhang, and we would like to thank Hongjia Chen and Naihuan Jing for interesting discussions.
报告2摘要：We used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra glm|n(C). The structures of the representations over the general linear Lie superalgebra and the special linear Lie superalgebra are studied in this paper. Then we extend the construction to the affine Kac–Moody Lie superalgebra case and Lie super-analogy EALA case on the tensor product of a polynomial algebra and an exterior algebra with infinitely many variables involving one parameter μ, and we also obtain the necessary and sufficient condition for the representations to be irreducible. In fact, the representation is irreducible if and only if the parameter μ is nonzero. This is a joint work with Hongjia Chen, Yun Gao and Ziting Zeng.