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.
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abstract
We analyse the geodesic E10/K(E10) sigma-model in a level decomposition w.r.t. the A8xA1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations of motion, when restricted to zeroth and first order spatial gradients, are shown to match with the sigma-model equations of motion up to level four. Remarkably, the self-duality of the five-form field strength is implied by E10 and the matching.
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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.