Epipelagic Langlands parameters and L-packets for unitary groups.

Reeder and Yu have recently given a new construction of a class of supercuspidal representations called epipelagic representations [M. Reeder and J.-K. Yu, Epipelagic representations and invariant theory, J. Amer. Math. Soc.27(2) (2014) 437–477, MR 3164986]. We explicitly calculate the Local Langlands Correspondence for certain families of epipelagic representations of unitary groups, following the general construction of Kaletha [Epipelagic L -packets and rectifying characters, Invent. Math.202(1) (2015) 1–89, MR 3402796]. The interesting feature of our computation is that we find simplifications within L -packets of the two novel invariants introduced in the above-mentioned paper of Kaletha, the toral invariant and the admissible L-embedding. [ABSTRACT FROM AUTHOR]