Reductions of Galois Representations for Slopes in (1, 2)

Shalini Bhattacharya, Eknath Ghate
We describe the semisimplifications of the mod p reductions of certain crystalline two-dimensional local Galois representations of slopes in (1, 2) and all weights. The proof uses the compatibility between the p-adic and mod p Local Langlands Correspondences for GL 2 (Q p). We also give a complete description of the submodules generated by the second highest monomial in the mod p symmetric power representations of GL 2 (F p).