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High Energy Physics - Theory, hep-th
Abstract:
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. We present explicit expressions for
all K(E10) elements that are associated to real roots of the hyperbolic algebra
(of which there are infinitely many), as well as novel explicit realizations of
the generators associated to imaginary roots and their multiplicities. We also
discuss the resulting realizations of the Weyl group.
