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A paper of Reederā€“Yu [J. Amer. Math. Soc. 27 (2014), pp. 437ā€“477] gives a construction of epipelagic supercuspidal representations of $p$-adic groups. The input for this construction is a pair $(\lambda , \chi )$ where $\lambda$ is a stable vector in a certain representation coming from a Moyā€“Prasad filtration, and ā€¦