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We describe the semi-simplification of the mod $p$ reduction of certaincrystalline two dimensional local Galois representations of slopes in theinterval $(1,2)$ and all weights. The proof uses the mod $p$ Local LanglandsCorrespondence for $GL_2(Q_p)$. We also give a complete description of thesubmodules generated by the second highest monomial in the mod $p$ symmetricpower representations of $GL_2(F_p)$.

Reductions of Galois representations for slopes in $(1,2)$