Investigating root multiplicities in the indefinite Kac-Moody algebra \(E_{10}\). (English) Zbl 1293.17031

Summary: Following a procedure outlined by Kang, we view the generalized eigenspaces, known as root spaces, of the infinite dimensional Kac-Moody algebra \(E_{10}\) as generalized eigenspaces for representations of the finite dimensional special linear algebra \(A_9\). Then, using the combinatorial representation theory of the special linear Lie algebras, we determine the dimensions of certain root spaces in \(E_{10}\).


17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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