11 citations · 17 across the 18 of their papers we have counts for
24 papers
Unitary Shimura Correspondence for Complex Classical Groups
Wan-Yu Tsai, Kayue Daniel Wong, Hongfeng Zhang
In this paper, we construct a lifting operator from the Grothendieck group of admissible Harish-Chandra modules of (resp. $\mathrm{Sp}_{2n}(\mathbb…
Vogan's FPP conjecture for complex Lie groups
Chao-Ping Dong, Kayue Daniel Wong
In this paper, we give a proof of Vogan's fundamental parallelepiped (FPP) conjecture for complex simple Lie groups, resulting in a reduction step in the classification of irreduci…
The unitary dual of
Kayue Daniel Wong, Hongfeng Zhang
In this paper, we give a full classification of the unitary dual of for . As a consequence, we determine which of these representations are weakly fair $A_{\…
On the Lefschetz Principle for and
Kei Yuen Chan, Kayue Daniel Wong
We construct an exact functor from the category of Harish-Chandra modules of to the category of finite-dimensional modules of graded Hecke algebras of ty…
Dirac series for complex
Dan Barbasch, Kayue Daniel Wong
In this paper, we classify all unitary representations with non-zero Dirac cohomology for complex Lie group of Type E8. This completes the classification of Dirac series for all co…
The genuine unitary dual of complex spin groups
Kayue Daniel Wong, Hongfeng Zhang
In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.
On some conjectures of the unitary dual of
Kayue Daniel Wong
In this manuscript, we introduce the notion of fundamental cases to study the unitary dual of . As applications, we prove of a conjecture of Salamanca-Riba and Vogan stated…
Admissible modules and normality of classical nilpotent orbits II
Dan Barbasch, Kayue Daniel Wong
In this paper, we compute the character formula of the Brylinski model for all classical nilpotent varieties . As a consequence, one can compute the multipl…
Dirac series for complex
Chao-Ping Dong, Kayue Daniel Wong
This paper classifies the Dirac series for complex . As applications, we verify a few conjectures raised in 2011, 2019 and 2020 for this exceptional Lie group. In particular,…
Dirac index of some unitary representations of and
Chao-Ping Dong, Kayue Daniel Wong
Let be or . We compute the Dirac index of a large class of unitary representations considered by Vogan in Section 8 of [Vog84], which include all…
Dirac series for complex classical Lie groups: A multiplicity-one theorem
Dan Barbasch, Chao-Ping Dong, Kayue Daniel Wong
This paper computes the Dirac cohomology of irreducible unitary Harish-Chandra modules of complex classical groups viewed as real reductive groups. More precisely, uni…
Dirac series of
Chao-Ping Dong, Kayue Daniel Wong
The unitary dual of was classified by Vogan in the 1980s. Focusing on the irreducible unitary representations of with half-integral infinite…
Scattered representations of complex classical Lie groups
Chao-ping Dong, Kayue Daniel Wong
This paper studies scattered representations of , and , which lies in the `core' of the unitary spectrum with…
On the Dirac Series of
Chao-ping Dong, Kayue Daniel Wong
This paper computes the Dirac index of all the weakly fair modules of . Although counter-examples have been found to a conjecture of Vogan on the uni…
Scattered representations of
Chao-Ping Dong, Kayue Daniel Wong
Let be . This paper aims to describe the Zhelobenko parameters and the spin-lowest -types of the scattered representations of , which lie at the heart…
Admissible modules and normality of classical nilpotent orbits I
Dan Barbasch, Kayue Daniel Wong
In the case of complex symplectic and orthogonal groups, we find modules with the property that their structure matches the structure of regular functions o…
Unipotent Representations of Exceptional Richardson Orbits
Kayue Daniel Wong
We study special unipotent representations attached to complex exceptional Richardson orbits. As a consequence, we verify a conjecture of Achar and Sommers for these orbits.
Special Unipotent Representations with Half Integral Infinitesimal Characters
Kayue Daniel Wong
For any special nilpotent orbit, let be one half of the semisimple element of a Jacobson-Morozov triple associated to the orbit. In 1985, Barbasch and Vogan d…
Some Calculations of the Lusztig-Vogan Bijection for Classical Nilpotent Orbits
Kayue Daniel Wong
In this manuscript, we compute explicitly the Lusztig-Vogan bijection for local systems of some classical, special, nilpotent orbits. Using these results, we prove a conjecture of…
On Quantization of a Nilpotent Orbit Closure in
Kayue Daniel Wong
Let be the complex exceptional Lie group of type . Among the five nilpotent orbits in its Lie algebra , only the 8-dimensional orbit has non-…
Regular Functions of Symplectic Spherical Nilpotent Orbits and their Quantizations
Kayue Daniel Wong
We study the ring of regular functions of classical spherical orbits for . In particular, treating as a real Lie group with maximal comp…
A Casselman-Osborne theorem for rational Cherednik algebras
Jing-Song Huang, Kayue Daniel Wong
We define Lie algebra cohomology associated with the half-Dirac operators for representations of rational Cherednik algebras and show that it has property described in the Casselma…
Local Systems on Classical Nilpotent Orbits and Maximal Length Elements
Kayue Daniel Wong
It is known that there is a bijection between dominant weights of a complex reductive Lie group and the set whose elements are of the form $(\math…
Quantization of Special Symplectic Nilpotent Orbits and Normality of their Closures
Kayue Daniel Wong
We study the regular function ring for all symplectic nilpotent orbits with even column sizes. We begin by recalling the quantization model for all s…