Isodual multiplicity-two tensor-product conjecture for rigid adelic spaces

Let $(E,\sigma)$ be an isodual rigid adelic space over a number field $K$ with automorphism group $G$. Assume that $E$ and $E^{\vee}$ are isomorphic as $K[G]$-modules, and that

$$E=\bigoplus_{i=1}^t V_i^{a_i}$$

where the $V_i$ are absolutely irreducible $G$-modules and $a_i\leq 2$. Isodual tensor-product conjecture. For every rigid analytic space $F$,

$$H_{\min}(E\otimes F)=H_{\min}(E)H_{\min}(F).$$

This is the proposed isodual counterpart of the multiplicity-free tensor-product theorem. The analogous description of invariant subspaces fails when multiplicities occur, so the conjecture remains unresolved under the stated multiplicity-two hypothesis.