## University of Sydney Algebra Seminar

# Sinéad Lyle (University of East Anglia)

## Friday 12th April, 12:05-12:55pm, Carslaw 373

### Symmetric group algebras, Khovanov-Lauda-Rouquier algebras and Specht modules

The Khovanov-Lauda-Rouquier algebras are certain \(\mathbb{Z}\)-graded algebra which have been shown to be isomorphic to the cyclotomic Hecke algebras of type \(G(l,1,n)\), one example of which is the symmetric group algebra. As a consequence, we have a grading on the symmetric group algebra. The Specht modules have been shown to be graded, so as a consequence, we may talk about graded decomposition numbers.

In this talk, we introduce the KLR algebras and discuss some aspects of their representation theory.