A note on tensor categories of Lie type E₉

الأصل · EN

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra (E₉). We describe an elementary algorithm for determining the decomposition of the submodule of 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 Eₙ, N=9.