Recursive multigraph-based constructions produce families of generalized Cartan matrices with exponentially growing coranks for Kac-Moody algebras, with explicit spectra computed via adjacency eigenvalue multiplicity.
E10 and a "small tension expansion" of M Theory
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abstract
A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.
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math.RA 1years
2026 1verdicts
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On a new class of high-corank Kac-Moody algebras
Recursive multigraph-based constructions produce families of generalized Cartan matrices with exponentially growing coranks for Kac-Moody algebras, with explicit spectra computed via adjacency eigenvalue multiplicity.