Speaker: Jieru Zhu
Affiliation: University of Queensland
Abstract
Kazhdan Lusztig polynomials, first defined in 1979 in purely algebraic terms, have found various incarnations in Lie theory, geometric representation theory, and diagrammatic categorification. It has remained one of the exciting topics in representation theory, with both Kazhdan-Lusztig conjecture and Lusztig’s conjecture unfolding in the past few decades. Despite collective efforts, combinatorial closed formulas have remained open except for lower rank cases, and are deemed very difficult to find.
In this talk, we will give a brief survey for a recent breakthrough in this area, i.e. a combinatorial closed formula for the parabolic/relative Kazhdan-Lusztig polynomial, for the antispherical module and the Hermitian symmetric pairs, by Bowman-De Visscher-Farrell-Hazi-Norton. This result uses Tempereley-Lieb diagrams and was also hinted in Khovanov’s thesis, with connections to dual canonical bases for the quantum group sl_2. In the end, we will mention some of my ongoing work in generalizing their work to the sl_3 case.
About Maths Colloquium
The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics.
We aim to present expository lectures that appeal to our wide audience.
Information for speakers
Information for speakers
Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.
Presentations are 50 minutes, plus five minutes for questions and discussion.
Available facilities include:
- computer
- data projector
- chalkboard or whiteboard
To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.