## Open problems in the theory of generalized standard Young tableaux

**Arun Ram**

Princeton University

[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!