Abstract
The Lorentzian Kac–Moody algebra E 11, obtained by doubly overextending the compact E 8, is decomposed into representations of its canonical hyperbolic E 10 subalgebra. Whereas the appearing representations at levels 0 and 1 are known on general grounds, higher level representations can currently only be obtained by recursive methods. We present the results of such an analysis up to height 120 in E 11 which comprises representations on the first five levels. The algorithms used are a combination of Weyl orbit methods and standard methods based on the Peterson and Freudenthal formulae. In the appendices we give all multiplicities of E 10 occurring up to height 340 and for E 11 up to height 240.
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