On regular square integrable representations of p-adic groups

We study the problem of construction of noncuspidal irreducible square integrable representations of classical p-adic groups, and questions related to it. Starting from cuspidal reducibilities in the generalized rank one case, we give a construction of regular irreducible square integrable representations of p-adic GSp (n), Sp(n) and SO(2n + 1). Under an assumption (expected to hold in general), we show that all such representations should come from this construction. Further, we obtain a number of general results about places where square integrable representations can appear in parabolically induced representation. Among others, we show that in irreducible cuspidal representations of general linear groups, only the self-contragredient ones play a role in the construction of square integrable representations of the above groups. At the end, we use our regular square integrable representations to study some basic properties of Whittaker models. We also show that there exists nondegenerate standard modules of classical groups which contain degenerate irreducible subrepresentations.