Let G be a connected complex simple Lie group, and let be the set of all equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology. We show that consists of two parts: finitely many scattered representations, and finitely many strings of representations. Moreover, the strings of come from via cohomological induction and they are all in the good range. Here L runs over the Levi factors of proper θ-stable parabolic subgroups of G. It follows that figuring out requires a finite calculation in total. As an application, we report a complete description of .
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11571097
Funding statement: The second-named author is supported by NSFC grant 11571097 and the China Scholarship Council.
In this appendix, we index all the involutions s in the Weyl group of by presenting the weight ; see Table 17.
The second-named author thanks the math department of MIT for offering excellent working conditions during October 2016 and September 2017. He is deeply grateful to the atlas mathematicians for many things, and to the referee for offering nice suggestions.
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