On the Dirac Series of $U(p,q)$

Chao-ping Dong; Kayue Daniel Wong

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arXiv · 2003.07165

On the Dirac Series of $U(p,q)$

Chao-ping Dong·Kayue Daniel Wong

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Abstract

This paper computes the Dirac index of all the weakly fair $A_{\mathfrak{q}}(\lambda)$ modules of $U(p, q)$. Although counter-examples have been found to a conjecture of Vogan on the unitary dual of $U(p, q)$ phrased by Trapa in 2001, we 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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BibTeX RIS

Chao-ping Dong, Kayue Daniel Wong. 2020-03-16. On the Dirac Series of $U(p,q)$. https://arxiv.org/abs/2003.07165

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