  Let $K$ be an arbitrary field of characteristic not equal to 2. Let $m,
n\in\N$ and $V$ an $m$ dimensional orthogonal space over $K$. There is a right
action of the Brauer algebra $\bb_n(m)$ on the $n$-tensor space $V^{\otimes n}$
which centralizes the left action of the orthogonal group $O(V)$. Recently G.I.
Lehrer and R.B. Zhang defined certain quasi-idempotents $E_i$ in $\bb_n(m)$
(see (\ref{keydfn})) and proved that the annihilator of $V^{\otimes n}$ in
$\bb_n(m)$ is always equal to the two-sided ideal generated by $E_{[(m+1)/2]}$
if $\ch K=0$ or $\ch K>2(m+1)$. In this paper we extend this theorem to
arbitrary field $K$ with $\ch K\neq 2$ as conjectured by Lehrer and Zhang. As a
byproduct, we discover a combinatorial identity which relates to the dimensions
of Specht modules over symmetric groups of different sizes and a new integral
basis for the annihilator of $V^{\otimes m+1}$ in $\bb_{m+1}(m)$.
