Huang's conjecture on parabolic induction from representations with nonzero Dirac cohomology

Let $G$ be a complex classical Lie group, and let a unitary representation of $G$ be given. A unitary representation has nonzero Dirac cohomology if its Dirac cohomology does not vanish. Huang's conjecture. A unitary representation either has nonzero Dirac cohomology or is induced from a unitary representation with nonzero Dirac cohomology by parabolic induction. The paper states that this conjecture, raised by Huang in 2015, is disproved for the groups studied; hence the proposed description of the unitary dual by parabolic induction from representations with nonzero Dirac cohomology is false.