Persitence of non degeneracy is a phenomenon which appears in the theory of
Q​l​-representations of the linear group: every irreducible
submodule of the restriction to the mirabolic subgroup of an non degenerate
irreducible representation is non degenerate. This is no more true in general,
if we look at the modulo l reduction of some stable lattice. As in the
Clozel-Harris-Taylor generalization of global Ihara's lemma, we show that this
property, called non degeneracy persitence, remains true for lattices given by
the cohomology of Lubin-Tate spaces