We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D = 11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional 'R symmetry' group K(E-9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E-10) is studied. We explain in detail how these representations are related to certain finite codimension ideals within K(E-9), which we exhibit explicitly, and how the known, as well as new finite-dimensional 'generalised holonomy groups' arise as quotients of K(E-9) by these ideals. In terms of the loop algebra realisations of E-9 and K(E-9) on the fields of maximal supergravity in two space-time dimensions, these quotients are shown to correspond to (generalised) evaluation maps, in agreement with previous results of [1]. The outstanding question is now whether the related unfaithful representations of K(E-10) can be understood in a similar way.