Simple representations of KLR algebras can be used to realize the infinity crystal for the corresponding symmetrizable Kac-Moody algebra. It was recently shown that, in finite and affine types, certain sub-categories of “cuspidal” representations realize crystals for sub-Kac-Moody algebras. Here we put that observation on a firmer categorical footing by exhibiting a corresponding functor betwee...

The unexpected and fascinating emergence of hyperbolic Coxeter groups and Lorentzian Kac-Moody algebras in the investigation of gravitational theories in the vicinity of a cosmological singularity is briefly reviewed. Some open questions raised by this intriguing result, and some attempts to answer them, are outlined. Dedicated to Claudio Bunster on the occasion of his 60th birthday. To appear ...

Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X , we show that if we expand X by extending X0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call “depth” and are supp...

Moody’s KMV method is a popular commercial implementation of the structural credit risk model pioneered by Merton (1974). It is an algorithm for estimating the unobserved asset value and the unknown parameters required for implementing such a model. This estimation method has found its way to the recent academic literature, but it has not yet been formally analyzed to assess its statistical pro...

Compactification can control chaotic Mixmaster behavior in gravitational systems with p–form matter: we consider this in light of the connection between supergravity models and Kac–Moody algebras. We show that different compactifications define “mutations” of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems ...

We study the “fermionic billiards”, i.e. the chaotic dynamics of the gravitino, that arise in the near-spacelike-singularity limit of elevendimensional supergravity and of its dimensional truncations (notably fourdimensional simple supergravity). By exploiting the gravity-coset correspondence, we show that the billiard dynamics of the gravitino is described by a ‘spin extension’ of the E10 Weyl...

We classify regular subalgebras of affine Kac–Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac–Moody algebras and conformally invariant subalgebras ...

In this paper, we look at long geometric progressions on diferent model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huf curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We fnd infnite families of twist...