University of Sydney Algebra Seminar

John Enyang (University of Sydney)

Friday 20th September, 12:05-12:55pm, Carslaw 373

Homomorphisms between cell modules of the Brauer algebra

In the generic or semisimple setting, for instance where \(z\) is an indeterminant, there are necessarily no non-zero homomorphisms between the cell modules of the Brauer algebra \( B_k(z)\). In analogy with the work of P. Martin on partition algebras, we show that the representation theory over a field of characteristic zero of non-generic specialisations \( B_k(n)\) of \(B_k(z)\), for \(n\in\mathbb{Z}\), is controlled by homomorphisms between the cell modules of \( B_k(n)\).

We then construct certain families of homomorphisms between cell modules of \(B_k(n)\) and use these homomorphisms to obtain associated decomposition numbers for the Brauer algebras.