arXiv subjects

Chao-ping Dong

Publications and source records attributed to Chao-ping Dong.

3 recordsLinked to original sources

arXiv2023

Spin Norm and Lambda Norm

Given a $K$-type $π$, it is known that its spin norm (due to first-named author) is lower bounded by its lambda norm (due to Vogan). That is, $\|π\|_{\rm spin}\geq \|π\|_{\rm lambda}$. This note aims to describe for which $π$ one can actually have equality. We apply the result to tempered Dirac series. In the case of real groups, we obtain that the tempered Dirac series are divided into $\#W^1$ parts among all tempered modules with real infinitesimal characters.

math.RT↗

arXiv2020

Scattered representations of complex classical Lie groups

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.

math.RT↗

arXiv2020

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

This paper computes the Dirac index of all the weakly fair $A_{\mathfrak{q}}(λ)$ 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 $A_{\mathfrak{q}}(λ)$ module.

math.RT↗