The symplectic ideal and a double centraliser theorem

• Autores: Rudolf Tange
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 687-699
• Idioma: inglés
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• Resumen

  • 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 , 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] of infinitesimal invariants in the algebra of regular functions on G is a unique factorisation domain.