Klima, Vicky; Shatley, Timothy; Thomas, Kyle; Wilson, Andrew Investigating root multiplicities in the indefinite Kac-Moody algebra \(E_{10}\). (English) Zbl 1293.17031 Involve 7, No. 4, 529-546 (2014). 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 \(E_{10}\). MSC: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Keywords:Kac-Moody; representation theory; combinatorial representation theory; root multiplicity PDF BibTeX XML Cite \textit{V. Klima} et al., Involve 7, No. 4, 529--546 (2014; Zbl 1293.17031) Full Text: DOI OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.