题目：Canonical Bases for Quantum gl_{m|n} and their Modified Version

报告人🕵🏼：Professor Jie Du （University of New South Wales）

地点：致远楼108室

时间🦹🏿‍♀️🦏：2024年8月3日 星期六 10:00-11:00

摘要♦︎：Using quantum differential operators, we construct a quantum gl_{m|n} supermodule structure on a certain polynomial superalgebra. We then extend this representation to its formal power series algebra which contains a submodule isomorphic to the regular representation of this quantum supergroup. In this way, we obtain a new presentation for quantum gl_{m|n} by a basis together with explicit multiplication formulas by generators. This allows us to introduce the canonical basis for the +-part.

On the other hand, we extend the supermodule structure on the polynomial superalgebra to a (partial) Laurent polynomial superalgebra which induces the regular representation of the modified quantum gl_{m|n}. In this way, a new presentation and its canonical basis theory are developed for this modified case.

This is joint work with Haixia Gu and Zhongguo Zhou.

欢迎各位参加🐍！