Linear algebra meets Lie algebra: the Kostant-Wallach theory
arXiv:0809.1204
Abstract
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
27 pages, LaTeX; abstract added