On the characters of Sylow $p$-subgroups of finite Chevalley groups $G(p^f)$ for arbitrary primes

We develop in this work a method to parametrize the set $\mathrm{I}\mathrm{r}\mathrm{r}(U)$ of irreducible characters of a Sylow $p$-subgroup $U$ of a finite Chevalley group $G(p^f)$ which is valid for arbitrary primes $p$, in particular when $p$ is a very bad prime for $G$. As an application, we parametrize $\mathrm{I}\mathrm{r}\mathrm{r}(U)$ when $G={\mathrm{F}}_4(2^f)$.