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Compression of root systems and the $$E$$-sequence. (English) Zbl 1206.17008
Summary: We examine certain maps from root systems to vector spaces over finite fields. By choosing appropriate bases, the images of these maps can turn out to have nice combinatorial properties, which reflect the structure of the underlying root system. The main examples are $$E_6$$ and $$E_7$$.

##### MSC:
 17B22 Root systems 17B25 Exceptional (super)algebras
##### Keywords:
visualising the root systems E6 and E7
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