Geometric configurations, regular subalgebras of E10 and M-theory cosmology

We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E10-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (nm,g3), n ≤ 10. We show that these solutions are associated with rank g regular subalgebras of E10, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E10.Fil: Henneaux, Marc. Vrije Unviversiteit Brussel; BélgicaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Vrije Unviversiteit Brussel; BélgicaFil: Persson, Daniel. Vrije Unviversiteit Brussel; BélgicaFil: Spindel, Philippe. Centro de Estudios Cientificos; Chil