John Enyang (University of Sydney)
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.
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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