  Let $m, n\in{\mathbb N}$. In this paper we study the right permutation action
of the symmetric group ${\mathfrak S}_{2n}$ on the set of all the Brauer
$n$-diagrams. A new basis for the free ${\mathbb Z}$-module ${\mathfrak B}_n$
spanned by these Brauer $n$-diagrams is constructed, which yields Specht
filtrations for ${\mathfrak B}_n$. 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
$V^{\otimes n}$ in the Brauer algebra ${\mathfrak B}_n(-2m)$. In particular, we
show that it is a ${\mathfrak S}_{2n}$-submodule of ${\mathfrak B}_n(-2m)$.
