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Journal of Lie Theory 20 (2010), No. 1, 017--030
Copyright Heldermann Verlag 2010

On Invariants of a Set of Elements of a Semisimple Lie Algebra

Ivan Losev
Dept. of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A.


\def\g{{\frak g}} \def\h{{\frak h}} \def\C{\mathbb{C}} Let $G$ be a complex reductive algebraic group, $\g$ its Lie algebra and $\h$ a reductive subalgebra of $\g$, $n$ a positive integer. Consider the diagonal actions $G:\g^n, N_G(\h):\h^n$. We study a connection between the algebra $\C[\h^n]^{N_G(\h)}$ and its subalgebra consisting of restrictions to $\h^n$ of elements of $\C[\g^n]^G$.

Keywords: Semisimple Lie algebras, conjugacy of embeddings, invariants of sets of elements in Lie algebras.

MSC: 17B20, 14R20, 14L30

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