Let \(\mathfrak {o}_l\) be a finite principal ideal local ring of length l. The degenerate Whittaker space associated with a representation of \(\textrm{GL}_{2n}(\mathfrak {o}_l)\) is a representation of \(\textrm{GL}_n(\mathfrak {o}_l)\) . For strongly cuspidal representations of \(\textrm{GL}_{2n}(\mathfrak {o}_l)\) the structure of degenerate Whittaker space is described by Prasad’s conjecture, which has been proven for \(\textrm{GL}_4(\mathfrak {o}_2)\) . In this paper, we describe the degenerate Whittaker space for certain induced representations of \(\textrm{GL}_4(\mathfrak {o}_2)\) , specifically those induced from subgroups analogous to the maximal parabolic subgroups of \(\textrm{GL}_4(\mathbb {F}_q)\) .
