# 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.