On higher spin realizations of K(E10)

Understand

Starting from the known unfaithful spinorial representations of the compact subalgebra K(E10) of the split real hyperbolic Kac-Moody algebra E10 we construct new fermionic `higher spin' representations of this algebra (for `spin-5/2' and `spin-7/2', respectively) in a second quantized framework.

• Our construction is based on a simplified realization of K(E10) on the Dirac and the vector spinor representations in terms of the associated roots, and on a re-definition of the vector spinor first introduced by Damour and Hillmann.
• The latter replaces manifestly SO(10) covariant expressions by new expressions that are covariant w.r.t.
• SO(1,9), the invariance group of the DeWitt metric restricted to the space of scale factors.