The University of Michigan Combinatorics Seminar
Crystal graphs are an especially nice way to encode the data one needs
to compute tensor product multiplicities for (say) irreps of semisimple
Lie groups or algebras. There are a number of known ways to generate
crystal graphs (e.g., Littelmann paths, or various flavors of tableaux
in the classical cases), but until now, there has not been a simple
intrinsic description of these graphs.