Branching rules for unramified principal series representations of GL(3) over a p-adic field

On restriction to the maximal compact subgroup $\mathrm{G}\mathrm{L}(3,\mathcal{R})$, an unramified principal series representation of the $p$-adic group $\mathrm{G}\mathrm{L}(3,F)$ decomposes into a direct sum of finite-dimensional irreducibles each appearing with finite multiplicity. We describe a coarser decomposition into components which, although reducible in general, capture the equivalences between the irreducible constituents.