[The basic preliminary concepts were introduced by N. Bergeron]
I will define some new combinatorial objects related to root systems and make a list of open problems in this theory. These new objects are generalizations of standard Young tableaux and their combinatorics gives information about the representation theory of affine Hecke algebras. Any solutions to the problems that I will pose would have interesting representation theoretic implications. There are many more problems than I have time to work on and I would be thrilled to have others take some of them up!