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For a rank two root system and a pair of nonnegative integers, using only elementary com-binatorics we construct two posets. The constructions are uniform across the root systems We then form the dis-tributive lattices of order ideals of these posets. Corollary 5.4 gives elegant quotient-of-products expressions for the rank generating functions of these… (More)

We associate one or two posets (which we call " semistandard posets ") to any given irreducible representation of a rank two semisimple Lie algebra over C. Elsewhere we have shown how the distributive lattices of order ideals taken from semis-tandard posets (we call these " semistandard lattices ") can be used to obtain certain information about these… (More)

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