Specht filtrations and tensor spaces for the Brauer algebra

Let m,n ∈ N. In this paper we study the right permutation action of the symmetric group S2n on the set of all the Brauer n-diagrams. A new basis for the free Z-module Bn spanned by these Brauer n-diagrams is constructed, which yields Specht filtrations for Bn. For any 2m-dimensional vector space V over a field of arbitrary characteristic, we give an explicit and characteristic-free description of the annihilator of the n-tensor space V⊗n in the Brauer algebra Bn(−2m). In particular, we show that it is a S2n-submodule of Bn(−2m).