Generalized principal series of representations of classical \(p\)-adic groups are representations of the form \(\delta \rtimes \sigma\), where \(\delta\) is an irreducible essentially square-integrable representation of a general linear group, \(\sigma\) is an irreducible square-integrable (i.e., a discrete series) representation of a classical group. For a strongly positive discrete series \(\sigma\), a complete composition series of the generalized principal series has been described by G. Muić [Isr. J. Math. 140, 157–202 (2004; Zbl 1055.22015)]. The author extends the subrepresentation results from the above paper to a larger class of generalized principal series. In this class, a discrete series representation \(\sigma\) is obtained by adding two consecutive elements in the Jordan block of a strongly positive representation, while \(\delta\) assures that possible discrete series subquotients of \(\delta \rtimes \sigma\) are of the same type as \(\sigma\).
The author obtains necessary and sufficient conditions, under which the induced representation of the studied form contains a discrete series subquotient. Furthermore, it is shown that if the generalized principal series, which belongs to the studied family, has a discrete series subquotient, then it has a discrete series subrepresentation.