#### Vol. 7, No. 4, 2014

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Investigating root multiplicities in the indefinite Kac–Moody algebra $E_{10}$

### Vicky Klima, Timothy Shatley, Kyle Thomas and Andrew Wilson

Vol. 7 (2014), No. 4, 529–546
##### Abstract

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 ${E}_{10}$.

##### Keywords
Kac–Moody, representation theory, combinatorial representation theory, root multiplicity
Primary: 17B67