Generalized triangle inequalities and their applications. (English) Zbl 1130.53037
Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 719-741 (2006).
Summary: We present a survey of our recent work on generalized triangle inequalities in infinitesimal symmetric spaces, nonpositively curved symmetric spaces and Euclidean buildings. We also explain how these results can be used to analyze some basic problems of algebraic group theory including the problem of decomposition of tensor products of irreducible representations of complex reductive Lie groups. Among the applications is a generalization of the Saturation Theorem of Knutson and Tao to Lie groups other than \(\mathrm{SL} (n,\mathbb C)\).
For the entire collection see [Zbl 1095.00005].
For the entire collection see [Zbl 1095.00005].
MSC:
| 53C35 | Differential geometry of symmetric spaces |
| 14L24 | Geometric invariant theory |
| 20E42 | Groups with a \(BN\)-pair; buildings |
| 20G15 | Linear algebraic groups over arbitrary fields |
| 22E46 | Semisimple Lie groups and their representations |
