Local newforms for generic representations of $p$-adic ${\mathrm{SO}}_{2n+1}$: Reduction

Abstract

We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of ${\mathrm{SO}}_{2n+1}$ then it is also non-zero for all irreducible generic representations of ${\mathrm{SO}}_{2n+1}$.

arXiv comment67 pages, with an appendix by Chi-Heng Lo