Brauer’s centralizer algebras
are finite dimensional algebras with a distinguished basis. Each Brauer centralizer
algebra contains the group algebra of a symmetric group as a subalgebra and the
distinguished basis of the Brauer algebra contains the permutations as a subset. In
view of this containment it is desirable to generalize as many known facts
concerning the group algebra of the symmetric group to the Brauer algebras as
possible. This paper studies the irreducible characters of the Brauer algebras
in view of the distinguished basis. In particular we define an analogue of
conjugacy classes, and derive Frobenius formulas for the characters of the Brauer
algebras. Using the Frobenius formulas we derive formulas for the irreducible
character of the Brauer algebras in terms of the irreducible characters of the
symmetric groups and give a combinatorial rule for computing these irreducible
characters.
