Schur-Weyl duality for orthogonal groups

Abstract

We prove Schur–Weyl duality between the Brauer algebra 𝔅n(m) and the orthogonal group Om(K) over an arbitrary infinite field K of odd characteristic. If m is even, then 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⊗ n in the Brauer algebra 𝔅n(m) is also given.