Construction of Steinberg type representations for reductive \(p\)-adic groups
Let \(F\) be a nonarchimedean field and \(G\) the group of \(F\)-points of a connected reductive group over \(F\). This paper gives a construction of certain discrete series representations of \(G\). The author generalizes and refines the method of Tadić for the construction of some discrete series representations of classical \(p\)-adic groups. The method relies on Jacquet module techniques and in this paper it is extended to a general reductive \(p\)-adic group. The author first defines representations of Steinberg type. These representations are defined in families. A family contains representations of different Levi subgroups of \(G\) and they are related to each other via a certain condition on the Jacquet modules. The author then develops a method for constructing such representations and to compute explicitly their Jacquet modules.
scientific article; zbMATH DE number 5071449