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.

Thanks

PGH

have a clueabout what's going on... – Michal Kotowski Jul 31 '11 at 20:18Pleaseformulate questions so that semi-experts can read them. For example, I am very interested in both representation theory and mathematical physics, and one of the ways I like to learn about related areas is by reading questions on MO. Your question is pretty much useless to me. Conversely, it's clear from your question that R. Borcherds is one expert who likely can help, and I see he has answered below. But perhaps others would also be able to contribute if you provided context, background, definitions, etc. – Theo Johnson-Freyd Nov 26 '11 at 5:02