A note on tensor categories of Lie type $E_9$

Details A note on tensor categories of Lie type $E_9$ A note on tensor categories of Lie type $E_9$

2004-06-07

arxiv.org/abs/math/0406122v2

J. of Algebra, 284 (2005) no. 1, 296-309

Mathematics

Representation Theory

Final published version

Scientific paper

10.1016/j.jalgebra.2004.08.014

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 $\Vn$ 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 $E_N$, $N\not=9$.

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