Abstract
In this note, we will construct three small unitary representations for each of the four simply-connected exceptional Lie groups G of real rank = 4. We will describe the restrictions of these representations to a maximal compact subgroup K of G, and will show they are multiplicity-free. The method of construction is by a continuation of the “quaternionic discrete series” for G. This works in more generality, and we will treat it fully in another paper, so we have only sketched the proofs here.
Dedicated to Bert Kostant, with admiration
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Gross, B.H., Wallach, N.R. (1994). A Distinguished Family of Unitary Representations for the Exceptional Groups of Real Rank = 4. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics, vol 123. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0261-5_10
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