Some Conjectures for Root Systems

We present a collection of conjectures relating to root systems (or, equivalently, to Lie groups) together with the evidence we possess in support of them. They may be regarded as generalizations of Dyson’s conjecture [J. Math. Phys. 3 (1962), pp. 140–156] and Mehta’s conjecture [Random Matrices, Academic Press, New York, 1967].