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have added a minimum on the level decompositon of the first fundamental rep of $E_{11}$ here.
Could that Mysterious Duality found by Vafa et al. feature in your account?
A beautiful duality was discovered by Iqbal, Neitzke and Vafa between compactifications of M-theory on tori and the second cohomology of some associated del Pezzo surfaces. Now the full cohomology of theses surfaces spans the root lattice of a Borcherds superalgebra. Henry-Labordere Julia and Paulot have shown that some truncations of these Borchers algebras provide a classification of p-forms coming from tori reduction of (massive) maximal supergravity. This classification matches the one of the E11 conjecture of Peter West. The Borcherds description was recently proven to be systematically derived from the split real form of E11 by Henneaux, Julia and Levie. (MathOverflow comment).
Presumably that last result is in E_11, Borcherds algebras and maximal supergravity.
Thanks for the pointer! HJL 10 is most useful. The discussion in 1.3 on p. 6 makes me hopeful that it’s their Borcherds’ algebra which is the right thing to act on the exceptional tangent bundle in 11d. For the fact that there is the immense richness of higher levels in $E_{11}$ is good for campfire speculation as to M-theory-the-grandiose, but that Borcherds algebra seems to contain exactly what we need for M-theory-the-concrete, which is really good to know.
I am trying to understand if there is any algebraic structure, Borcherds or otherwise, that is represented on a low level truncation of the fundamental of $E_{11}$. Some text seemed to suggest this, but maybe not.
Shouldn’t it say ’0d supergravity’ (whatever that is) rather than
As U-duality group of 1d supergravity
Woops. Yes! Thanks for catching this silly typo. Fixed now.
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