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p-adic Hecke operators in the Iwahori-Hecke algebra $C_c(J\backslash G(F)/J)$

$\DeclareMathOperator\ch{ch}$Let $F$ be a non-archimedean local field, $\mathcal{O}$ its ring of integers, $\mathfrak{p}$ its maximal ideal and $\pi$ a uniformizer. I shall use $\kappa(F)$ to denote t …