## University of Sydney Algebra Seminar

# Andrew Mathas (University of Sydney)

## Friday 23 March, 12:05-12:55pm, Carslaw 175

### Quiver Schur algebras and decomposition numbers

Brundan and Kleshchev have shown that the degenerate and non-degenerate Hecke algebras of type \(G(r,1,n)\) are \(\mathbf{Z}\)-graded. This puts a very rigid structure on the module categories of these algebras which is hard to work with but also provides a wealth of new information. I will describe how to extend the KLR grading on the Hecke algebras to the cyclotomic Schur algebras and also how to use these gradings to compute decomposition numbers of certain blocks, both in characteristic zero and in positive characteristic. This is joint work with Jun Hu.