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

On restriction to the maximal compact subgroup GL(3,R), an unramified principal series representation of the p-adic group GL(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.