Brauer algebra dual modules and polytabloids

This paper fills in the relationship between the standard and dual representations of irreducible Brauer algebra modules in all cases, semisimple and non-semisimple. This parallels the correspondence given in earlier works for the constructions of the Specht modules. In addition, due to the close relationship between Brauer algebra irreducible modules in the non-semisimple case and certain multiplications, some general work on polytabloids is discussed. This gives an extension to previous results about the non-semisimple case.