Uniform bounds and uncertainty for asymptotics of representations of $p$-adic ${\mathrm{GL}}_N$

Rahul Dalal, Mathilde Gerbelli-Gauthier, Simon Marshall

We prove two results on the growth of dimensions of fixed vectors of representations $\ddot{I}€$ of $p$-adic ${\mathrm{GL}}_N$ under principal congruence subgroups: First, a uniform bound on t…