Bertram Kostant

Abstract:   Recently, using Gelfand-Zeitlin and the space of Hessenberg matrices, Wallach and I found natural Darboux coordinates (as a classical mechanical solution of the Gelfand-Kirillov question) on g for the case where g is the space of all matrices. Now, at least locally, I do the same for any g using results of A. A. Tarasov on Fomenko-Miscenko theory and old results of mine on a generalization of the Hessenberg matrices.

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