On convexity, the Weyl group and the Iwasawa decomposition

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1. [1] S. ARAKI, On root systems and an infinitesmal classification of irreducible symmetric spaces (J. of Math, Osaka City Univ., vol. 13, 1962, p. 1-34). Zbl0123.03002MR27 #3743
2. [2] S. HELGASON, Differential Geometry and Symmetric Spaces, Academic Press, New-York, 1962. Zbl0111.18101MR26 #2986
3. [3] A. HORN, Doubly stockastic matrices and the diagonal of a rotation matrix (Amer. J. Math, vol. 76, 1954, p. 620-630). Zbl0055.24601MR16,105c
4. [4] J. E. HUMPHREYS, Introduction to Lie algebras and representation theory, Springer-Verlag, 1972. Zbl0254.17004MR48 #2197
5. [5] N. IWAHORI and I. SATAKE, On Cartan subalgebras of a Lie algebra, Kodai Math Seminar Report, N° 3, 1950, p. 51-60. Zbl0045.01102MR12,585c
6. [6] B. KOSTANT, The principal three dimensional subgroups and the Betti numbers of a complex semi-simple Lie group (Amer. J. Math., vol. 81, 1959, p. 973-1032). Zbl0099.25603MR22 #5693
7. [7] B. KOSTANT, Lie group representations on polynomial rings (Amer. J. Math., vol. 86, 1963, p. 327-402). Zbl0124.26802MR28 #1252
8. [8] B. KOSTANT and S. RALLIS, Orbits and representations associated with symmetric spaces (Amer. J. Math., vol. 93, 1971, p. 753-809). Zbl0224.22013MR47 #399
9. [9] A. LENARD, Generalization of the Golden-Thompson Inequality, Tr eA eB tr eA+B (Indiana Univ. Math. J., vol. 21, 1971, p. 457-467). Zbl0215.08606MR44 #6724
10. [10] O. LOOS, Symmetric Spaces, I. General Theory, Benjamin, 1969. Zbl0175.48601MR39 #365a
11. [11] G. D. MOSTOW, Some new decomposition theorem for semi-simple Lie groups (Memoirs of the A. M. S., N° 14, 1955). Zbl0064.25901MR16,1087g
12. [12] Classification de Groupes de Lie algebriques, (Séminaire C. Chevalley, 1956-1958, vol. I). 
13. [13] M. SUGIURA, Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras (J. Math Soc., vol. 11, 1959, p. 374-434). Zbl0204.04201MR26 #3827
14. [14] C. THOMPSON, Inequalities and partial orders on matrix spaces (Indiana Univ. Math. J., vol. 21, 1971, p. 469-480). Zbl0227.15005MR45 #3442
15. [15] F. WARNER, Foundations of Differential Manifolds and Lie Groups, Scott, Foresman and Company. Zbl0241.58001
16. [16] A. HORN, On the eigenvalues of a matrix with prescribed singular values, Proceedings of the Amer. Math. Soc., vol. 5, 1954, p. 4-7. Zbl0055.00908MR15,847d

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