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Minimal linear Morse functions on the orbits in Lie algebras

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Abstract

It is proved that all Morse height functions on regular orbits of the adjoint action of compact semisimple Lie groups are perfect. In the case of an arbitrary linear representation of a compact Lie group it is proved that all height functions satisfy the Bott property on the orbits of the representation. The case of the group SO4 is considered in more details.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    V. A. Shmarov

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  1. V. A. Shmarov
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Correspondence to V. A. Shmarov.

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Original Russian Text © V.A. Shmarov, 2015, published in Vestnik Moskovskogo Universitetam Matematika. Mekhanika, 2015, Vol. 70, No. 2, pp. 9–16.

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Shmarov, V.A. Minimal linear Morse functions on the orbits in Lie algebras. Moscow Univ. Math. Bull. 70, 60–67 (2015). https://doi.org/10.3103/S0027132215020023

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