Cones, crystals, and patterns (Q1128341)

This work describes an interpretation of the Gelfand-Tsetlin patterns in terms of crystal graphs and generalizes such patterns to arbitrary complex semisimple algebraic groups. For each element of the crystal basis, the author gets a sequence of integers. He then considers the cone \(C\) spanned by all such sequences. In some cases \(C\) has a simple description. He finds a description in terms of the root ordering for all rank two Kac-Moody algebras.