Abstract
We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac–Moody algebra g ( E 9 ) . We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗ n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann's path algorithm and conforms with the uniform combinatorial behavior recently discovered by H. Wenzl for the series E N , N ≠ 9 .
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