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Journal of the London Mathematical Society Advance Access originally published online on March 11, 2008
Journal of the London Mathematical Society 2008 77(3):687-699; doi:10.1112/jlms/jdm108
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© 2008 London Mathematical Society

The symplectic ideal and a double centraliser theorem

Rudolf Tange

Fakultät für Mathematik
Ruhr-Universität Bochum
Universitätsstrasse 150
D-44780 Bochum
Germany
rudolf.tange@rub.de

We interpret a result of Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on Formula , where V is the natural module for the symplectic group. This result was obtained in characteristic zero by Weyl. Furthermore, we use this to extend to arbitrary connected reductive groups G with simply connected derived group the earlier result of the author that the algebra K[G]g of infinitesimal invariants in the algebra of regular functions on G is a unique factorisation domain.

2000 Mathematics Subject Classification 14L35, 20G15.

Received May 11, 2007; revised September 14, 2007; published online March 11, 2008.


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