On K(E9)
Abstract
We study the maximal compact subgroup K(E9) of the affine Lie group E9(9) and its on-shell realization as an R symmetry of maximal N=16 supergravity in two dimensions. We first give a rigorous definition of the group K(E9), which lives on the double cover of the spectral parameter plane, and show that the infinitesimal action of K(E9) on the chiral components of the bosons and the fermions is determined in terms of an expansion of the Lie algebra of K(E9) about the two branch points of this cover; this implies in particular that the fermions of N=16 supergravity transform in a spinor representation of K(E9). The fermionic equations of motion can be fitted into the lowest components of a single K(E9) covariant `Dirac equation', with the linear system of N=16 supergravity as the gauge connection. These results suggest the existence of an `off-shell' realization of K(E9) in terms of an infinite component spinor representation. We conclude with some coments on `generalized holonomies' of M theory.
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