SMS scnews item created by John Enyang at Wed 18 Sep 2013 1333
Type: Seminar
Distribution: World
Expiry: 20 Sep 2013
Calendar1: 20 Sep 2013 1205-1255
CalLoc1: Carslaw 373
Auth: enyang@penyang.pc (assumed)

# Homomorphisms between cell modules of the Brauer algebra

### Enyang

###### Speaker:

John Enyang (University of Sydney)

###### Title:

Homomorphisms between cell modules of the Brauer algebra

###### Abstract:

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.

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We will go to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang John.Enyang@sydney.edu.au

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