On reducibility points beyond ends of complementary series of p-adic GL(n)

Abstract: In this paper we consider reducibility points beyond the ends of complementary series of general linear groups over a p-adic field, which start with Speh representations. We describe explicitly the composition series of the representations at these reducibility points. They are multiplicities one representations, and they can be of arbitrary length. We give Langlands parameters of all the irreducible subquotients.