Proves that if newform spaces are non-zero for all irreducible generic supercuspidal representations of SO(2n+1), then they are non-zero for all irreducible generic representations.
Atobe, The set of local A-packets containing a given representation , Journal für die reine und angewandte Mathematik , vol
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Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Reduction
Proves that if newform spaces are non-zero for all irreducible generic supercuspidal representations of SO(2n+1), then they are non-zero for all irreducible generic representations.