Schur-Weyl duality for orthogonal groups

Abstract

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.

35 pages; to appear in Proc. L.M.S

References in corpus (1)

• The blocks of the Brauer algebra in characteristic zero

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