Lattice Bounds for Compact Semisimple Lie Groups identifies a structural feature of compact Lie groups and their representations. In concrete terms, it formalizes the statement that let be a compact connected semisimple Lie group, let be a maximal torus, and let be the TR X^(T) g CTQRP g G g T GTC Z( G) G/CC LCC Z( G)Q$..