Quaternionic discrete series representation

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).

Quaternionic representations are analogous to holomorphic discrete series representations, which exist when the symmetric space of the group has a complex structure.

References

• Gross, Benedict H.; Wallach, Nolan R (1994), "A distinguished family of unitary representations for the exceptional groups of real rank =4", in Brylinski, Jean-Luc; Brylinski, Ranee; Guillemin, Victor; Kac, Victor (eds.), Lie theory and geometry, Progr. Math., vol. 123, Boston, MA: Birkhäuser Boston, pp. 289–304, ISBN 978-0-8176-3761-3, MR1327538
• Gross, Benedict H.; Wallach, Nolan R (1996), "On quaternionic discrete series representations, and their continuations", Journal für die reine und angewandte Mathematik, 481: 73–123, doi:10.1515/crll.1996.481.73, ISSN 0075-4102, MR1421947