Ennola duality conjecture for character degrees of general linear and unitary congruence quotients

Let $n\in\mathbb{N}$. For $\varepsilon\in\{-1,1\}$, let $\mathfrak{o}$ be a compact discrete valuation ring with residue cardinality $q$, let $\mathsf{G}$ be one of the $\mathfrak{o}$-group schemes $\mathsf{GL}_n$ or $\mathsf{GU}_n$, and write $\varepsilon=\varepsilon_{\mathsf{G}}$ accordingly. Ennola duality conjecture. There exist a finite index set $I$, polynomials $f_i^{(\varepsilon)}\in\mathbb{Z}[1/n!][t]$ and $g_i^{(\varepsilon)}\in\mathbb{Z}[t]$, ascending chains of finite sets $\mathcal{B}_{i,1}\subset\mathcal{B}_{i,2}\subset\cdots\subset\mathbb{N}$, and non-negative integers $A_{ij}^{(\varepsilon)},B_{ij}$ such that, for every $\ell\in\mathbb{N}$, the character degrees and representation zeta function of $\mathsf{G}(\mathfrak{o}_\ell)$ are respectively

$$\operatorname{cd}(\mathsf{G}(\mathfrak{o}_\ell))=\{g_i^{(\varepsilon)}(q)q^{B_{ij}\mid i\in I,j\in\mathcal{B}_{i,\ell}}\},$$

and

$$\zeta_{\mathsf{G}(\mathfrak{o}_\ell)}(s)=\sum_{i\in I}\sum_{j\in\mathcal{B}_{i,\ell}}f_i^{(\varepsilon)}(q)q^{A_{ij}^{(\varepsilon)}}\left(g_i^{(\varepsilon)}(q)q^{B_{ij}}\right)^{-s}.$$

Moreover, for every $i\in I$, Ennola duality holds for character degrees:

$$g_i^{(-1)}(t)=(-1)^{\deg(g_i^{(1)})}g_i^{(1)}(-t).$$

The conjecture extends the observed uniformity of character degrees and zeta functions for finite congruence quotients of general linear and unitary groups; the cited low-level and low-rank cases are known, while the asserted uniform description for all $n$ and levels remains open.