LAUSR

This paper computes the Dirac index of all the weakly fair $$A_{{\mathfrak {q}}}(\lambda )$$ A q ( λ ) modules of U ( p ,  q ). We find counter-examples to a conjecture of Vogan on the unitary dual of U ( p ,  q ), which was phrased by Trapa in 2001. However, we still believe that any irreducible unitary representation of U ( p ,  q ) with non-zero Dirac cohomology must be a weakly fair $$A_{{\mathfrak {q}}}(\lambda )$$ A q ( λ ) module.