Conjugation in Brauer algebras and applications to character theory

Details Conjugation in Brauer algebras and applications to character theory Conjugation in Brauer algebras and applications to character theory

2009-11-27

arxiv.org/abs/0911.5271v1

Mathematics

Representation Theory

33 pages

Scientific paper

The Brauer algebra has a basis of diagrams and these generate a monoid $H$ consisting of scalar multiples of diagrams. Following a recent paper by Kudryavtseva and Mazorchuk, we define and completely determine three types of conjugation in $H$. We are thus able to define modular characters for Brauer algebras which share many of the properties of Brauer characters defined for finite groups over a field of prime characteristic. Furthermore, we reformulate and extend the theory of ordinary characters for Brauer algebras as introduced by Ram to the case when the Brauer algebra is not semisimple.

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