IIB supergravity and E10

We analyze the geodesic E10/K(E10)σ-model in a level decomposition w.r.t. the A8×A1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations of motion, when restricted to zeroth and first order spatial gradients, are shown to match with the σ-model equations of motion up to level ℓ=4. Remarkably, the self-duality of the five-form field strength is implied by E10 and the matching.