The Newform $K$-Type and $p$-adic Spherical Harmonics

Peter Humphries

Let $K:={\mathrm{GL}}_n(\mathcal{O})$ denote the maximal compact subgroup of ${\mathrm{GL}}_n(F)$, where $F$ is a nonarchimedean local field with ring of integers $\mathcal{O}$. We s…