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. 


1. Is this 16 homomorphic (or related) to E8 X E8 in string theory?
2. 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.


Thanks


PGH



Bimonster and Heterotic String Theory
The connection between the bimonster and moonshine and the 26 dimensions of string theory is still mysterious (at least to me), though there are several intriguing hints that there is something going on. 


Some papers discussing this are as follows: 


The paper by Miyamoto
"21 involutions acting on the Moonshine module" J . Algebra 175 (1995), no. 3, 941–965. 
gives a relation between the 26 involutions generating the bimonster and the natural module of the monster. His construction involves the 26 dimensional even unimodular Lorentzian lattice that also appears in string theory and moonshine. 


Basak "The complex Lorentzian Leech lattice and the Bimonster" J. Algebra 309 (2007), no. 1, 32–56 gives a complex reflection group generated by 26 complex reflections similar to the bimonster, except that the generators have order 3 rather than 2. 


