×

zbMATH — the first resource for mathematics

On convexity, the Weyl group and the Iwasawa decomposition. (English) Zbl 0293.22019

MSC:
22E15 General properties and structure of real Lie groups
22E30 Analysis on real and complex Lie groups
15A18 Eigenvalues, singular values, and eigenvectors
15A42 Inequalities involving eigenvalues and eigenvectors
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[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). MR 27 #3743 | Zbl 0123.03002 · Zbl 0123.03002
[2] S. HELGASON , Differential Geometry and Symmetric Spaces , Academic Press, New-York, 1962 . MR 26 #2986 | Zbl 0111.18101 · Zbl 0111.18101
[3] A. HORN , Doubly stockastic matrices and the diagonal of a rotation matrix (Amer. J. Math, vol. 76, 1954 , p. 620-630). MR 16,105c | Zbl 0055.24601 · Zbl 0055.24601
[4] J. E. HUMPHREYS , Introduction to Lie algebras and representation theory , Springer-Verlag, 1972 . MR 48 #2197 | Zbl 0254.17004 · Zbl 0254.17004
[5] N. IWAHORI and I. SATAKE , On Cartan subalgebras of a Lie algebra , Kodai Math Seminar Report, N^\circ 3, 1950 , p. 51-60. Article | MR 12,585c | Zbl 0045.01102 · Zbl 0045.01102
[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). MR 22 #5693 | Zbl 0099.25603 · Zbl 0099.25603
[7] B. KOSTANT , Lie group representations on polynomial rings (Amer. J. Math., vol. 86, 1963 , p. 327-402). MR 28 #1252 | Zbl 0124.26802 · Zbl 0124.26802
[8] B. KOSTANT and S. RALLIS , Orbits and representations associated with symmetric spaces (Amer. J. Math., vol. 93, 1971 , p. 753-809). MR 47 #399 | Zbl 0224.22013 · Zbl 0224.22013
[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). MR 44 #6724 | Zbl 0215.08606 · Zbl 0215.08606
[10] O. LOOS , Symmetric Spaces, I. General Theory , Benjamin, 1969 . MR 39 #365a | Zbl 0175.48601 · Zbl 0175.48601
[11] G. D. MOSTOW , Some new decomposition theorem for semi-simple Lie groups (Memoirs of the A. M. S., N^\circ 14, 1955 ). MR 16,1087g | Zbl 0064.25901 · Zbl 0064.25901
[12] Classification de Groupes de Lie algebriques , (Séminaire C. Chevalley, 1956 - 1958 , vol. I). Numdam · Zbl 0092.26301
[13] M. SUGIURA , Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras (J. Math Soc., vol. 11, 1959 , p. 374-434). MR 26 #3827 | Zbl 0204.04201 · Zbl 0204.04201
[14] C. THOMPSON , Inequalities and partial orders on matrix spaces (Indiana Univ. Math. J., vol. 21, 1971 , p. 469-480). MR 45 #3442 | Zbl 0227.15005 · Zbl 0227.15005
[15] F. WARNER , Foundations of Differential Manifolds and Lie Groups , Scott, Foresman and Company. Zbl 0241.58001 · Zbl 0241.58001
[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. MR 15,847d | Zbl 0055.00908 · Zbl 0055.00908
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.