Dirac cohomology, branching laws and Wallach modules.

The idea of using Dirac cohomology to study branching laws was initiated by Huang, et al. (2013) [11]. 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 E 6 (− 14) and E 7 (− 25) : we recover the K -spectrum of the Wallach modules from their Dirac cohomology. [ABSTRACT FROM AUTHOR]