Composition series of generalized principal series; the case of strongly positive discrete series
This paper is devoted to the study of the structure of certain representations of either the symplectic groups or full orthogonal groups over a \(p\)-adic field, \(F\). Let \(R(G)\) denote the Grothendieck group of representations of finite length of groups in the tower; let \(R(GL)\) be the Grothendieck group of representations of finite length of a general linear group. There is a natural map, due to Tadić, from \(R(G)\) to \(R(G) \otimes R(GL(n))\). This arises as the maximal parabolic subgroup of the group \(G_n\) of split rank \(n\) in the tower has Levi component \(GL(j,F) \times G_{n-j}\). The purpose of this paper is to determine the composition series of induction from a parabolic subgroup, the representation on the \(G_n\) factor is a strongly positive discrete series representation. The representations of the general linear groups are relatively well understood. The final results are complete but too intricate to be summarized here.
scientific article; zbMATH DE number 2114398