Abstract
Using the sharpened Helgason–Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of E7(−5). As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of E7(−5). Assuming the infinitesimal character being integral, we further improve the Helgason–Johnson bound for E7(−5). This should help people to understand (part of) the unitary dual of this group.
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