ORBITS OF EXCEPTIONAL GROUPS, DUALITY AND BPS STATES IN STRING THEORY

We give an invariant classification of orbits of the fundamental repre sentations of the exceptional groups E-7(7) and E-6(6) which classify BPS states in string and M theories toroidally compactified to d = 4 a nd 5. The exceptional Jordan algebra and the exceptional Freudenthal t riple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d = 5 and d = 4, respectively. The classifi cation of BPS states preserving different numbers of supersymmetries i s in close parallel to the classification of the little groups and the orbits of timelike, lightlike and spacelike vectors in Minkowski spac e. The orbits of BPS black holes in N = 2 Maxwell-Einstein supergravit y theories in d = 4 and d = 5 with symmetric space geometries are also classified including the exceptional N = 2 theory, which has E7(-25) and E6(-26) as its symmetry in the respective dimensions.