A. The Bimonster and the Complex Lorentzian Leech Lattice involves a construction that extends Y555 from 16 to 26, and relates to Incidence(P^2/F3) among other things. (13 projective points + 13 projective lines), Complex Lorentzian Leech Lattice as Hyperbolic cell 2 + 24 dimensions, etc.
B. How does this relate to the 26 dimensions of Bosonic String Theory (Where 26 dimensions of the Lorentzian Leech Lattice (IIsub(25,1)) which is a torus in 24 dimensions orbifolded over a 2-point reflection group....and collapses from 26 to 10 dimensions using E8 X E8, one version of heterotic string theory...
The confusion lies in that this (B.) is 10 + 16 = 26 (or 26 dimensions collapsed down to 10), and the Bimonster situation (A.) is 16 nodes of the Dynkin diagram Y555 (or M666) of M X M wreath built up (with some difficulties) to 26 nodes of Inc(P2/F3) if I understand it right.
- Is this 16 homomorphic (or related) to E8 X E8 in string theory?
- Is the 2-point reflection group in bosonic string theory the same as the hyperbolic cell discussed in the Bimonster construction? Z2 in E8 X E8 is apparently the identification of the common boundaries of E8 X E8... I am fascinated by both A and B and would like more clarification of their relationships.