Schur–Weyl duality for orthogonal groups
Schur–Weyl duality for orthogonal groups
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DOI：
10.1112/plms/pdn044
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发表时间：
2007-12
影响因子：
1.8
通讯作者：
S. Doty;Jun Hu
中科院分区：
文献类型：
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作者：
S. Doty;Jun Hu
证明了任意奇特征无限域K上Brauer代数n（m）与正交群Om（K）之间的Schur-Weyl对偶性.如果m是偶数，那么我们证明了正交么半群的每个连通分支都是正规簇;这意味着与单位分支相关联的正交Schur代数是广义Schur代数。作为主要结果的一个应用，给出了Brauer代数n（m）中n张量空间V n的零化子的一个无特征的显式描述.
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.