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Let $G$ be the adjoint group of $\\mathfrak{g}$ and let $K$ be the connected Lie subgroup of $G$ with Lie algebra $ad(\\mathfrak{k})$. If $U(\\mathfrak{g})$ is the universal enveloping algebra of $\\mathfrak{g}$ then $U(\\mathfrak{g})^K$ will denote the centralizer of $K$ in $U(\\mathfrak{g})$. 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