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Proceedings of the London Mathematical Society Advance Access originally published online on November 5, 2008
Proceedings of the London Mathematical Society 2009 98(3):679-713; doi:10.1112/plms/pdn044
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© 2008 London Mathematical Society

Schur–Weyl duality for orthogonal groups

Stephen Doty

Department of Mathematics and Statistics
Loyola University Chicago
6525 North Sheridan Road
Chicago, IL 60626
USA
doty@math.luc.edu

Jun Hu

Department of Applied Mathematics
Beijing Institute of Technology
Beijing 100081
People's Republic of China

Received 25 November 2007.

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{otimes} n in the Brauer algebra Bn(m) is also given.

2000 Mathematics Subject Classification 20G05 (primary), 20C20 (secondary).

The second author was supported by the National Natural Science Foundation of China (Project 10771014), the Program NCET and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.


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