  In U-duality-manifest formulations, supergravity fields are packaged into
covariant objects such as the generalized metric and $p$-form fields
$\mathcal{A}_p^{I_p}$. While a parameterization of the generalized metric in
terms of supergravity fields is known for U-duality groups $E_n$ with $n\leq
8$, a parameterization of $\mathcal{A}_p^{I_p}$ has not been fully determined.
In this paper, we propose a systematic method to determine the parameterization
of $\mathcal{A}_p^{I_p}$, which necessarily involves mixed-symmetry potentials.
We also show how to systematically obtain the T- and S-duality transformation
rules of the mixed-symmetry potentials entering the multiplet. As the simplest
non-trivial application, we find the parameterization and the duality rules
associated with the dual graviton. Additionally, we show that the 1-form field
$\mathcal{A}_1^{I_1}$ can be regarded as the generalized graviphoton in the
exceptional spacetime.
