We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

In the study of conjecture on M-theory as a non-linear realization E11/K11 we present arguments for the following: 1)roots of K11 coincide with the roots of Kac-Moody algebra EE11 with Dynkin diagram given in the paper, 2)one of the fundamental weights of EE11 coincides with l1 weight of E11, known to contain 11d supergravity brane charges. The statement 1) is extended on E10 and E9 algebras. E...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

We introduce both idiosyncratic and aggregate shocks in an endogenous growth model with endogenous partial insurance to the idiosyncratic shock. Aggregate uncertainty introduces an additional channel that can play an important role in determining the effects of private information on expected growth and asset prices. We show the impact of aggregate and idiosyncratic shocks on expected growth an...

We show that compactifications of the heterotic string on a circle exhibit at boundary moduli space ($R\to 0$, or equivalently decompactification limit $R \to \infty$) tower winding momentum modes enhance $E_8 \times E_8$ $SO(32)$ gauge symmetry to affine algebras $(E_9 \oplus E_9)/\sim$ (the identification means two copies $E_9$ share same central extension) and $\hat{D}_{16}$, respectively. a...