On an algebraic approach to the Zelevinsky classification for classical p-adic groups

In this paper we classify irreducible, admissible representations of p-adic classical groups in a purely algebraic way. We present a new and simple algorithm for constructing the classifying data which is also useful in other contexts where the computation with Jacquet modules or constant terms of Eisenstein series appears. We construct and study non-standard intertwining operators. They are defined in a purely algebraic way although their rationality follows from [G. Muić, A geometric construction of intertwining operators for reductive p-adic groups, Manuscripta Math. 125 (2008) 241–272].