  A modular or distributive lattice is `diamond-colored' if its order diagram
edges are colored in such a way that, within any diamond of edges, parallel
edges have the same color. Such lattices arise naturally in combinatorial
representation theory, particularly in the study of poset models for semisimple
Lie algebra representations and their companion Weyl group symmetric functions.
One of our goals is to gather in one place some elementary but foundational
results concerning these lattice structures; this includes some new results as
well as some new interpretations of classical results. We then develop many
points of contact between diamond-colored modular/distributive lattices and
combinatorial Lie representation theory, leading to some new Dynkin diagram
classification results and some new results concerning minuscule and
quasi-minuscule representations.
