Kobayashi's conjecture on associated varieties holds for (e6(-14), so(8,1)) with the minimal holomorphic representation, and no discrete series is admissible for non-holomorphic Klein four pairs of exceptional Hermitian type.
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Kobayashi's conjecture on associated varieties for $(\mathrm{E}_{6(-14)},\mathrm{Spin}(8,1))$
Kobayashi's conjecture on associated varieties holds for (e6(-14), so(8,1)) with the minimal holomorphic representation, and no discrete series is admissible for non-holomorphic Klein four pairs of exceptional Hermitian type.