AIS - Representation Theory of Quivers and BGG Category O for semi simple Lie Algebras (2024)

Venue: IIT Kanpur, online mode

Dates: 2 Dec 2024 to 21 Dec 2024


Convener(s)

 
Name: Amit Kuber Sachin Sharma
Mailing Address: Associate Professor
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
Uttar Pradesh 208016
Associate Professor
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
Uttar Pradesh 208016
Email: askuber at iitk.ac.in sachinsh at iitk.ac.in

Representation theory of quivers(=finite-dimensional associative algebras) and Lie algebras are classical yet active topics of study and research, both having diverse applications in various branches of mathematics as well as theoretical physics. The two areas are interconnected but the former is underrepresented in India. The purpose of this school is to introduce the former area to the students and researchers from the Indian community while also building up the Lie theory side up to BGG Category O where quivers appear naturally. A more fundamental connection between the two can be seen via Dynkin diagrams, which appear in the classification of hereditary finite dimensional algebras (Gabriel’s theorem) as well as semisimple Lie algebras.

In the former theme, we will cover Gabriel’s theorem and Auslander-Reiten theory in the first two weeks while a guest speaker, Thomas Brustle, will introduce more contemporary topics to the audience. The latter theme will comprise of the basics of highest weight modules of semisimple Lie algebras in the first two weeks leading up to the Bernstein-Gelfand-Gelfand  (BGG) category O. This workshop will provide a unique opportunity as well as a common platform for students and researchers interested in either area.