We prove Schur--Weyl duality between the Brauer algebra $\mathfrak{ B}_n(m)$ and the orthogonal group $O_{ m}(K)$ over an arbitrary infinite field $K$ of odd characteristic. If $m$ is even, we show that each connected component of the orthogonal monoid is a normal variety; this implies that the orthogonal Schur algebra associated to the identity component is a generalized Schur algebra. As an application of the main result, an explicit and characteristic-free description of the annihilator of $n$-tensor space $V^{ \otimes n}$ in the Brauer algebra $mathfrak{ B}_n(m)$ is also given.
Categories: math.RT math.GR