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 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