| Summary: | Abstract We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E 11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use finite-dimensional fermionic representations of the R-symmetry K(E 11) to describe the fermionic contributions to the duality equations. These duality equations reduce to the known equations of E 8 exceptional field theory or eleven-dimensional supergravity for appropriate (partial) solutions of the section constraint. Of key importance in the construction is an indecomposable representation of E 11 that entails extra non-dynamical fields beyond those predicted by E 11 alone, generalising the known constrained p-forms of exceptional field theories. The construction hinges on the tensor hierarchy algebra extension of e 11 $$ {\mathfrak{e}}_{11} $$ , both for the bosonic theory and its supersymmetric extension.
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