Decompositions of Hyperbolic Kac-Moody Algebras with Respect to Imaginary Root Groups.

We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac-Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group (2, 1), these imaginary root subgroups act on the complex Kac-Moody algebra viewed as a Hilbert space. We illustrate our new view on Kac-Moody groups by considering the example of a rank-two hyperbolic algebra that is related to the Fibonacci numbers.

Consistent Kaluza-Klein Truncations and Two-Dimensional Gauged Supergravity.

We consider generalized Scherk-Schwarz reductions of E_{9} exceptional field theory to D=2 space-time dimensions and, in particular, construct the resulting scalar potential of all gauged supergravities that can be obtained in this way. This provides the first general expression for a multitude of theories with an interesting structure of vacua, covering potentially many new AdS_{2} cases. As an application, we prove the consistency of the truncation of eleven-dimensional supergravity on S^{8}×S^{1} to SO(9) gauged maximal supergravity.

Symmetries of Post-Galilean Expansions.

In this Letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a nonrelativistic or post-Galilean expansion of the Poincaré symmetry. We find an infinite-dimensional vector space on which this generalized Galilei group acts and usual Minkowski space can be modeled by our construction. We also construct particle and string actions that are invariant under these transformations.