In his monumental book, Arthur gave a complete description of the automorphic discrete spec-
tra of quasi-split orthogonal groups and symplectic groups. Following Arthur, Mok obtained same
results for quasi-split unitary groups. To generalize these results to non quasi-split groups, one way
is to use the stable trace formula. In the 2014 paper of Kaletha-Minguez-Shin-White, they carried
out some results for inner forms of unitary groups in this way.
However, there is a much more cheaper way to “transport” these results from one group to another
group, which is provided by the theta lifts. In this talk, I will describe how we use the
theta lifts to get some results for non quasi-split even orthogonal or unitary groups.
Locally, we obtain a local Langlands correspondence; and globally, we obtain a multiplicity formula
for the tempered part of discrete spectra. The idea comes from Gan-Ichino’s paper "The Shimura-Waldspurger correspondence for $Mp_{2n}$" . If time permits, I will also briefly describe some related works.