Minimal linear Morse functions on orbits in Lie algebras / V. A. Shmarov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 2. P. 9-16 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 60-67].
A theorem stating that all Morse height functions are perfect on regular orbits of the
adjoint action of compact semisimple Lie groups is proved. In the case of arbitrary linear representation of
a compact Lie group we prove that all height functions are Bott functions on orbits of representation.
The case of
Key words: Lie group, Lie algebra, adjoint action, orbit, height function, perfect Morse function.