Induced representations of \(U\)(2,2) over a \(p\)-adic field (Q2757866)

Let \(G\) denote the quasi-split unitary group in four variables over a non-archimedean local field of characteristic zero. The paper gives a list of all irreducible constituents of representations of \(G\) parabolically induced from irreducible supercuspidal representations. There are three parabolic subgroups of \(G\) to be considered. For one of them, with Levi subgroup \(\text{U}(2)\times E^{\times}\), the L-function of the inducing representation is needed to determine reducibility of the induced representation. That L-function is computed by base change from \(\text{U}(2)\) to \(\text{GL}(2,E)\), using Shahidi's theorem on \(\gamma\)-factors. The case of the other maximal parabolic subgroup was treated by Goldberg. The case of the Borel group is extensively treated here. The unitarizable representations are also determined.