In mathematics, a **quaternionic discrete series representation** is a discrete series representation of a semisimple Lie group *G* associated with a quaternionic structure on the symmetric space of *G*. They were introduced by Gross and Wallach (1994, 1996).

Quaternionic discrete series representations exist when the maximal compact subgroup of the group *G* has a normal subgroup isomorphic to SU(2). Every complex simple Lie group has a real form with quaternionic discrete series representations. In particular the classical groups SU(2,*n*), SO(4,*n*), and Sp(1,*n*) have quaternionic discrete series representations.

Quaternionic representations are analogous to holomorphic discrete series representations, which exist when the symmetric space of the group has a complex structure. The groups SU(2,*n*) have both holomorphic and quaternionic discrete series representations.