# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### On KE(9)

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

0407055.pdf

(Preprint), 241KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Nicolai, H., & Samtleben, H. (2005). On KE(9).* Quarterly
Journal of Pure and Applied Mathematics,* *1*, 180-204.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4E5A-2

##### Abstract

We study the maximal compact subgroup K(E_9) of the affine Lie group E_9(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(E_9), which lives on the double cover of the spectral parameter plane, and show that the infinitesimal action of K(E_9) on the chiral components of the bosons and the fermions is determined in terms of an expansion of the Lie algebra of K(E_9) 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(E_9). The fermionic equations of motion can be fitted into the lowest components of a single K(E_9) 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(E_9) in terms of an infinite component spinor representation. We conclude with some coments on `generalized holonomies' of M theory.