16 citations · 44 across the 17 of their papers we have counts for
17 papers
Special unipotent representations of simple linear Lie groups of type A
Dan Barbasch, Jia-Jun Ma, Binyong Sun +1
Let G be a special linear group over the real, the complex or the quaternion, or a special unitary group. In this note, we determine all special unipotent representations of G in t…
Genuine special unipotent representations of spin groups
Dan Barbasch, Jia-Jun Ma, Binyong Sun +1
We determine all genuine special unipotent representations of real spin groups and quaternionic spin groups, and show in particular that all of them are unitarizable. We also show…
Special unipotent representations of real classical groups: counting and reduction
Dan Barbasch, Jia-Jun Ma, Binyong Sun +1
Let be a real reductive group in Harish-Chandra's class. We derive some consequences of theory of coherent continuation representations to the counting of irreducible represent…
On the notion of metaplectic Barbasch-Vogan duality
Dan Barbasch, Jia-Jun Ma, Binyong Sun +1
In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This…
Local theta correspondence: the basic theory
Binyong Sun, Chen-Bo Zhu
We give an elementary introduction to Classical Invariant Theory and its modern extension "Transcending Classical Invariant Theory", commonly known as the theory of local theta cor…
Local theta correspondence and nilpotent invariants
Chen-Bo Zhu
We consider two types of nilpotent invariants associated to smooth representations, namely generalized Whittaker models, and associated characters (in the case of a real reductive…
Special unipotent representations of real classical groups: construction and unitarity
Dan Barbasch, Jia-Jun Ma, Binyong Sun +1
Let be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit of , the Langlands dual of (or th…
Local theta lifting of generalized Whittaker models associated to nilpotent orbits
Raul Gomez, Chen-Bo Zhu
Let be a reductive dual pair over a local field ${\Fontauri k}$ of characteristic 0, and denote by and the standard modules of and ,…
Vanishing of quasi-invariant generalized functions
Dihua Jiang, Binyong Sun, Chen-Bo Zhu
Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this n…
Degenerate principal series of metaplectic groups and Howe correspondence
Soo Teck Lee, Chen-Bo Zhu
The main purpose of this article is to supplement the authors' results on degenerate principal series representations of real symplectic groups with the analogous results for metap…
Conservation relations for local theta correspondence
Binyong Sun, Chen-Bo Zhu
We prove Kudla-Rallis conjecture on first occurrences of local theta correspondence, for all type I irreducible dual pairs and all local fields of characteristic zero.
Fourier transform and rigidity of certain distributions
Binyong Sun, Chen-Bo Zhu
Let be a finite dimensional vector space over a local field, and be its dual. For a closed subset of , and of , consider the space of tempered…
A note on special orthogonal groups following Waldspurger
Binyong Sun, Chen-Bo Zhu
The purpose of this note is to verify that the archimedean multiplicity one theorems shown for orthogonal groups (as well as general linear and unitary groups) in a previous paper…
Uniqueness of Bessel models: the archimedean case
Dihua Jiang, Binyong Sun, Chen-Bo Zhu
In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.
Uniqueness of Ginzburg-Rallis models: the Archimedean case
Dihua Jiang, Binyong Sun, Chen-Bo Zhu
In this paper, we prove the uniqueness of Ginzburg-Rallis models in the archimedean case. As a key ingredient, we introduce a new descent argument based on two geometric notions at…
A general form of Gelfand-Kazhdan criterion
Binyong Sun, Chen-Bo Zhu
We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an…
Theta lifting of nilpotent orbits for symmetric pairs
Kyo Nishiyama, Hiroyuki Ochiai, Chen-bo Zhu
We consider a reductive dual pair (G, G') in the stable range with G' the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K'_C-orbits, where…