Base change for ramified unitary groups: the strongly ramified case (Q2030083)

In the unitary group case, describing the Langlands parameters of \(L\)-packets of discrete series is equivalent to describing their base changes. The local Langlands correspondence for packets of supercuspidal representations of unramified quasi-split unitary groups has been described by the second author in [Am. J. Math. 140, No. 6, 1567--1638 (2018; Zbl 1446.22005)]. The paper under review complements that result, and the authors compute a base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both over a \(p\)-adic field of odd residual characteristic. The base change is described in terms of canonical lifting of underlying simple character and the base change of the level-zero component of its inducing type.