Let $G$ be a split connected reductive group over $\mathbb{ Z}$. Let $F$ be a non-archimedean local field. With $K_m: = Ker(G(\mathfrak{ O}_F) \rightarrow G(\mathfrak{ O}_F/\mathfrak{ p}_F^m))$, Kazhdan proved that for a field $F'$sufficiently close local field to $F$, the Hecke algebras $\mathcal{ H}(G(F),K_m)$ and $\mathcal{ H}(G(F'),K_m')$ are isomorphic, where $K_m'$ denotes the corresponding object over $F'$. In this article, we generalize this result to general connected reductive groups.
Categories: math.RT