Generalized diffeomorphisms for E9

We construct generalized diffeomorphisms for E9 exceptional field theory. The transformations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalized diffeomorphism algebra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordinate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalized Scherk-Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.