Abstract
We give a computer-free proof of a theorem of Basak, describing the group generated by 16 complex reflections of order 3, satisfying the braid and commutation relations of the Y 555 diagram. The group is the full isometry group of a certain lattice of signature ( 13 , 1 ) over the Eisenstein integers Z [ 1 3 ] . Along the way we enumerate the cusps of this lattice and classify the root and Niemeier lattices over Z [ 1 3 ] .
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