A classification of Breuil modules

Abstract

Let p be a prime number and f a positive integer with f < p. In this paper, we determine the structure of simple Breuil modules of type $$ \oplus _{i = 1}^n\omega _f^{{k_i}}$$ corresponding to n-dimensional irreducible representations of $${G_{{{\bf{Q}}_p}}}$$ . We also describe the extensions of those simple Breuil modules if they correspond to mod p reductions of strongly divisible modules that correspond to Galois stable lattices in potentially semistable representations of $${G_{{{\bf{Q}}_p}}}$$ with Hodge-Tate weights {0, 1, …, n − 1} and Galois type $$ \oplus _{i = 1}^n\widetilde\omega _f^{{k_i}}$$ .