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 script G_2n on the set of all the Brauer n-diagrams. A new basis for the free ℤ-module ℬ_n spanned by these Brauer n-diagrams is constructed, which yields Specht filtrations for ℬ_n. 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 ℬ_n(-2m). In particular, we show that it is a script G_2n-submodule of ℬ_n(-2m).