Graded dimensions and cocenters of the cyclotomic KLR algebras

讲座时间 Datetime: 2022年9月24日，星期六， 10:10-11:10

地点 Venue: 腾讯线上会议：946-628-9201

主持人 Host：黄敏

报告人 Speaker: 胡峻 

单位 Affiliation: 北京理工大学

报告摘要 Abstract:

The KLR algebras and their cyclotomic quotients play important role in the categorification of quantum groups and their integrable highest weight modules. In this talk, I shall present a closed formula (discovered by Lei Shi and me) for the graded dimension  of the cyclotomic KLR algebras  associated to an arbitrary symmetrizable Cartan matrix.  I shall also report our recent progress on the characterization of the minimal degree and maximal degree components of the cocenter of these cyclotomic KLR algebra via a new object called "piecewise dominant sequences".