Decomposition numbers of Brauer algebras in non-dividing characteristic

We determine decomposition matrices of Brauer algebras over a field of characteristic 0 and for fields of prime characteristic p with p larger than the degree of the Brauer algebra. We reprove and extend work of Martin as well as by Cox and De Visscher over the complex field by using new methods which uniformly treat the characteristic 0 and prime characteristic cases. These methods are inspired by the theory of Jucys-Murphy elements and the use of refined induction and restriction functors which are generalizations of similar functors for symmetric groups.