For tame reductive p-adic groups with residue field of at least four elements, a Yu-type input without the second genericity condition induces a finite set of irreducible supercuspidal representations.
Winter, The automorphism group of an extraspecial p-group, Rocky Mountain J
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Construction of tame supercuspidal representations in arbitrary residue characteristic
For tame reductive p-adic groups with residue field of at least four elements, a Yu-type input without the second genericity condition induces a finite set of irreducible supercuspidal representations.