A note on tensor categories of Lie type E9

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac–Moody algebra g(E9). 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 Littelmannʹs path algorithm and conforms with the uniform combinatorial behavior recently discovered by H. Wenzl for the series EN, N≠9.