Abstracct:
Let p be a prime and n a positive integer. On the one hand, one can consider representations on characteristic p vector spaces of the topological group GL_n(Q_p), where Q_p is the field of p-adic integers. On the other hand, one can consider representations on characteristic p vector spaces of dimension n of the absolute Galois group of Q_p. We will illustrate a conjectural duality between these two kinds of representations, in the simplest case (so-called `p-small’). The talk will be mainly an introduction to the relevant set up.