The idea of using Dirac cohomology to study branching laws was initiated by Huang, Pandzi\'c and Zhu in 2013 [HPZ]. One of their results says that the Dirac cohomology of π completely determines π|K, where π is any irreducible unitarizable highest weight (g, K) module. This paper aims to develop this idea for the exceptional Lie groups E₆₍₋₁₄₎ and E₇₍₋₂₅₎: we recover the K-spectrum of the Wallach modules from their Dirac cohomology.
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Dong et al. (2024) studied this question.
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