Diagonalization in compact Lie algebras and a new proof of a theorem of Kostant

Wildberger, N. J.

doi:10.1090/S0002-9939-1993-1151817-6

Diagonalization in compact Lie algebras and a new proof of a theorem of Kostant
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Proc. Amer. Math. Soc. 119 (1993), 649-655 Request permission

Abstract:

We exhibit a simple algorithmic procedure to show that any element of a compact Lie algebra is conjugate to an element of a fixed maximal abelian subalgebra. An estimate of the convergence of the algorithm is obtained. As an application, we provide a new proof of Kostant’s theorem on the projection of orbits onto a maximal abelian subalgebra.

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