  Let G be a p-adic reductive group, and R an algebraically closed field. Let
us consider a smooth representation of G on an R-vector space V. Fix an open
compact subgroup K of G and a smooth irreducible representation of K on a
finite-dimensional R-vector space W. The space of K-homomorphisms from W to V
is a right module over the intertwining algebra H(G,K,W). We examine how those
constructions behave when we pass to the contragredient representations of V
and W, and we give conditions under which the behaviour is the same as in the
case of complex representations. We take an abstract viewpoint and use only
general properties of G. In the last section, we apply this to the theory of
types for the group GL(n) and its inner forms over a non-Archimedean local
field.
