Schur-Weyl duality for orthogonal groups

Details Schur-Weyl duality for orthogonal groups Schur-Weyl duality for orthogonal groups

2007-12-06

arxiv.org/abs/0712.0944v3

Mathematics

Representation Theory

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

Scientific paper

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.

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