Problems in Lie Group Theory

The theory of Lie groups and representations was developed by Lie, Killing, Cartan, Weyl and others to a degree of quasi-perfection, in the years 1870-1930 >. The main topological features of compact simple Lie groups were elucidated in the 40s by H. Hopf, Pontriagin and others. The exceptional groups were studied by Chevalley, Borel, Freudenthal etc. in 1949-1957. Torsion in the exceptional groups was considered by Toda, Adams etc. in the 80s. However, one can still ask some questions for which the answer is either incomplete or absent, at least to this speaker. We would like to raise and discuss some of them in this communication.