INTERTWINING MAPS BETWEEN p-ADIC PRINCIPAL SERIES OF p-ADIC GROUPS

In this paper we study p-adic principal series representation of a p-adic group G as a module over the maximal compact subgroup G0. Weshow that there are no non-trivial G0 -intertwining maps between principal series representations attached to characters whose restrictions to the torus of G0 are distinct, and there are no non-scalar endomorphisms of a fixed principal series representation. This is surprising when compared with another result which we prove: that a principal series representation may contain infinitely many closed G0 -invariant subspaces. As for the proof, we work mainly in the setting of Iwasawa modules, and deduce results about G0 -representations by duality.