Graded Rouquier blocks for Hecke and Schur algebras

Perhaps the most basic object in the world of representation theory is the symmetric group, the group of all ways of rearranging a set of size n. Despite the simplicity of this object, it is still very rich, and its category of representations is a remarkable mixture of combinatorial accessibility, and exceptionally difficult questions. Famously, the dimensions of simple representations over the symmetric group over finite fields (and their generalizations, decomposition numbers) are devilishly hard to compute.

In recent years, work of many authors has uncovered a new and surprising property of the group algebras of symmetric groups and their generalizations, Ariki-Koike algebras: they possess a grading. We aim to study this grading in a sector of the representation theory of AK algebras which is relatively simple: the Rouquier blocks. These were introduced relatively recently in the case of AK algebras, and thus much remains to be learned about them.

Faculty Supervisor:

Dror Bar-Natan

Student:

Partner:

University of Sydney

Discipline:

Mathematics

Sector:

Education

University:

University of Toronto

Program: