The local character expansion as branching rules: nilpotent cones and the case of $\mathrm{SL}(2)$

Monica Nevins

We show there exist representations of each maximal compact subgroup $K$ of the $p$-adic group $G=\mathrm{SL}(2,F)$, attached to each nilpotent coadjoint orbit, such that every irr…