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On quaternionic discrete series representations, and their continuations. (English) Zbl 0857.22012

We consider quaternionic discrete series and their unitary continuations, when \(G\) is a simple real Lie group and the symmetric space \(G/K\) has an invariant quaternionic structure. These representations can be constructed in analytic cohomology of degree 1, of homogeneous vector bundles on the twistor space covering of \(G/K\). As a corollary, we construct the minimal unitary representations for the exceptional Lie groups of real rank 4.

MSC:

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
22E15 General properties and structure of real Lie groups
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