# Branching rules for ramified principal series representations of GL3 over a p-adic field - Mathematics > Representation Theory

Abstract: We decompose the restriction of ramified principal series representations ofthe $p$-adic group $\mathrm{GL}3,\mathrm{k}$ to its maximal compact subgroup$K=\mathrm{GL}3,\mathscr{R}$. Its decomposition is dependent on the degree oframification of the inducing characters and can be characterized in terms offiltrations of the Iwahori subgroup in $K$. We establish several irreducibilityresults and illustrate the decomposition with some examples.

Author: Peter S. Campbell, Monica Nevins

Source: https://arxiv.org/