The symplectic ideal and a double centraliser theorem
Commutative Algebra
2014-02-26 v1 Representation Theory
Abstract
We interpret a result of S. Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on \bigoplus_{r=0}^s\otimes^rV, where V is the natural module for the symplectic group. This result was obtained in characteristic zero by H. 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.
Cite
@article{arxiv.0705.0377,
title = {The symplectic ideal and a double centraliser theorem},
author = {Rudolf Tange},
journal= {arXiv preprint arXiv:0705.0377},
year = {2014}
}