Dirac index of some unitary representations of $Sp(2n, \mathbb{R})$ and $SO^*(2n)$
Chao-Ping Dong,
Kayue Daniel Wong
Abstract:Let G be Sp(2n, R) or SO * (2n). We compute the Dirac index of a large class of unitary representations considered by Vogan in Section 8 of [32], which include all weakly fair Aq(λ) modules and (weakly) unipotent representations of G as two extreme cases. We conjecture that these representations exhaust all unitary representations of G with nonzero Dirac cohomology. In general, for certain irreducible unitary module of an equal rank group, we clarify the link between the possible cancellations in its Dirac ind… Show more
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