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For standard Young tableaux, semistandard Young tableaux, and other related two-dimensional arrays of numbers like plane partitions. Including their combinatorial theory and their application in representation theory and algebraic geometry.

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Decomposing tensor powers of the fundamental representation of exceptional Lie algebras

For the $A$-series, tensor powers of the fundamental representation of $\frak{sl}_n$ decompose into irreducibles according to a certain Young diagram/ partition formula. This inspires, for example, th …