Abstract
This paper computes the Dirac index of all the weakly fair \(A_{{\mathfrak {q}}}(\lambda )\) 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 \(A_{{\mathfrak {q}}}(\lambda )\) module.
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Funding
Dong was supported by the National Natural Science Foundation of China (grant 11571097, 2016-2019). Wong is supported by the National Natural Science Foundation of China (grant 11901491) and the Presidential Fund of CUHK(SZ).
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Dong, CP., Wong, K.D. On the Dirac series of U(p, q). Math. Z. 298, 839–859 (2021). https://doi.org/10.1007/s00209-020-02641-2
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DOI: https://doi.org/10.1007/s00209-020-02641-2