B10NonAbBlcksETH · Representation Theory of Blocks of Group Algebras with Non-abelian Defect Groups

The proposed project is set in pure mathematics in the areas of representation theory of associative algebras and Lie theory. Its goal is to contribute to the structure theory of the blocks of group algebras of symmetric groups with non-abelian defect groups. The main emphasis of this project will be on the subclass of the RoCK blocks. The main objective of the project is to make a significant contribution towards proving Turner's conjecture about the structure of the RoCK blocks.Recent developments from Lie theory and higher representation theory opened up completely new perspectives. The inspiration for the current proposal comes from the connections of the representation theory of symmetric groups to the representation theory of Kac-Moody algebras. Our approach to the above families of algebras will involve representation theoretical, combinatorial, homological and computational methods. These methods will represent a combination of classical methods, whose origin is in the work of James, and new methods originating in Kac-Moody algebras and quantum groups. Justification of such a choice of methods lies in the fact that this is one of the ground-breaking approaches that has the potential to produce very important results in a short time span.The proposed project will build on a very recent breakthroughs, it is extremely timely and will be a contribution to central open problems in the field. Even partial results will have a significant impact in the field and may lead to interesting developments.The subject is one of European excellence and the project will contribute greatly to the preservation of European dominance in the field.This research will be the starting point for a long-term research project and a scientific collaboration between the scientist in charge and Bogdanic, which will extend far beyond the duration of this fellowship, and it will be crucial for Bogdanic's career and his development as an independent researcher.