What are open problems in representation theory?

What are the sources (books/papers/sites) discussing this?

Any kinds of problems/questions are welcome - big/small, vague/concrete. Some estimation of difficulty and importance, as well as, small description, prerequisites and relevant references, ... are welcome.

To the best of my knowledge, there are NO good lists of representation theory problems on the web. E.g. the sites below contain lots of unsolved problem in other areas, but not in representation theory:

http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics

http://maven.smith.edu/~orourke/TOPP/

MO questions also discuss other fields, but not representation theory:

What are the big problems in probability theory?

What are some open problems in algebraic geometry?

What are some open problems in toric varieties?

Open problems with monetary rewards

Open problems in Euclidean geometry?

Open Questions in Riemannian Geometry

What are some of the big open problems in 3-manifold theory?

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