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

Abstract

On restriction to the maximal compact subgroup $\mathrm{GL}(3,\mathcal{R})$, an unramified principal series representation of the $p$-adic group $\mathrm{GL}(3,F)$ 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.

24 pages

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