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arXiv · 2006.07806

Scattered representations of complex classical Lie groups

Chao-ping Dong·Kayue Daniel Wong
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Abstract

This paper studies scattered representations of $G = SO(2n+1, \mathbb{C})$, $Sp(2n, \mathbb{C})$ and $SO(2n, \mathbb{C})$, which lies in the `core' of the unitary spectrum $G$ with nonzero Dirac cohomology. We describe the Zhelobenko parameters of these representations, count their cardinality, and determine their spin-lowest $K$-types. We also disprove a conjecture raised in 2015 asserting that the unitary dual can be obtained via parabolic induction from irreducible unitary representations with non-zero Dirac cohomology.

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BibTeXRIS

Chao-ping Dong, Kayue Daniel Wong. 2020-06-14. Scattered representations of complex classical Lie groups. https://arxiv.org/abs/2006.07806

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