Consistent truncation and generalized duality based on exceptional generalized cosets

We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\text{GS}\mathrm{\backslash }G\mathrm{/}H$. This approach generalizes the well-established generalized Scherk-Schwarz reductions on generalized parallelizable spaces $G\mathrm{/}H$, which preserve maximal supersymmetry, to scenarios with reduced supersymmetry by introducing a non-trivial generalized structure group $\text{GS}$. The double coset structure plays two distinct roles: for a given $G$, the choice of subgroup $\text{GS}$ determines the (constant) generalized torsion/curvature and the pattern of supersymmetry breaking, while $H$ parameterizes inequivalent supergravity backgrounds that share the same truncated theory. The entire construction proceeds algebraically, systematically building $\text{GS}$-invariant tensors from generalized frame fields, with the intrinsic torsion automatically constant and a $\text{GS}$-singlet. Different choices of $H$ lead to distinct higher-dimensional backgrounds that truncate to the same lower-dimensional theory, thereby realizing U-duality. We illustrate the framework through explicit examples in double field theory and exceptional field theory.