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.