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7 Kac–Moody Billiards II – The Case of Non-Split Real Forms

We will now make use of the results from the previous section to extend the analysis of Kac–Moody billiards to include also theories whose U-duality symmetries are described by algebras 𝔲 3 that are non-split. The key concepts are that of restricted root systems, restricted Weyl group – and the associated concept of maximal split subalgebra – as well as the Iwasawa decomposition already encountered above. These play a prominent role in our discussion as they determine the billiard structure. We mainly follow [95Jump To The Next Citation Point].

 7.1 The restricted Weyl group and the maximal split “subalgebra”
  The restricted Weyl group
  The maximal split “subalgebra” 𝖋
  The Iwasawa decomposition and scalar coset Lagrangians
 7.2 “Split symmetry controls chaos”
  7.2.1 (BC )1 and 𝒩 = 2, D = 4 pure supergravity
  7.2.2 Heterotic supergravity and 𝔰𝔬(8,24 )
 7.3 Models associated with non-split real forms

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