Abstract:Let G = GLn be the general linear group over an algebraically closed field k, let g = gl n be its Lie algebra and let U be the subgroup of G which consists of the upper uni-triangular matrices. Let k[g] be the algebra of polynomial functions on g and let k[g] G be the algebra of invariants under the conjugation action of G. We consider the problem of giving finite homogeneous spanning sets for the k[g] G -modules of highest weight vectors for the conjugation action on k[g]. We prove a general result in arbitra… Show more
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