Dongwen Liu

activity

20102026

most citedTheta functions and arithmetic quotients of loop groups

294 citations · 328 across the 36 of their papers we have counts for

collaborators

Showing math.RTShow all

25 papers · 1 filter

math.RT2026

Rankin--Selberg integrals of opposite conductor--one newforms

Dongwen Liu, Lei Zhang

Let $F$ be a nonarchimedean local field of characteristic zero and let $n \geq 2$ . For $r = n, n + 1$ , let $Π_{r}$ be an irreducible tempered representation of $GL_{r} (F)$ of conductor…

math.RT2026

Betti-Whittaker periods of the contragredient representations for $GL (n)$

Yubo Jin, Dongwen Liu, Binyong Sun

We define Betti-Whittaker periods for a broad class of cohomological automorphic representations and establish a relation between the periods associated with these representations…

math.RT2026

Fourier positivity for spherical functions I: split tori and spherical principal series

Michael Björklund, Dongwen Liu, Jun Yu +1

We prove Fourier positivity for spherical functions on a semisimple linear algebraic group $G$ over a local field restricted to its split tori $A$ for unitary principal series para…

math.RT2026

Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character

Dihua Jiang, Dongwen Liu, Zhikang Luo +2

In this paper, we establish in Theorem 1.2 the reciprocity of wavefront sets for irreducible admissible representations $π$ of classical groups $G$ over any local field $F$ of char…

math.RT2024

Archimedean period relations for Rankin-Selberg convolutions

Yubo Jin, Dongwen Liu, Binyong Sun

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $GL (n) \times GL (n)$ and $GL (n) \times GL (n - 1)$ , for all generi…

math.RT2023

Irreducible representations of $GL_{n} (C)$ of minimal Gelfand-Kirillov dimension

Zhanqiang Bai, Yangyang Chen, Dongwen Liu +1

In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of $G = GL_{n} (C)$ p…

math.RT2023

Arithmetic Branching Law and generic $L$ -packets

Cheng Chen, Dihua Jiang, Dongwen Liu +1

Let $G$ be a classical group defined over a local field $F$ of characteristic zero. For any irreducible admissible representation $π$ of $G (F)$ , which is of Casselman-Wallach type…

math.RT2022

Strong integrality of inversion subgroups of Kac-Moody groups

Abid Ali, Lisa Carbone, Dongwen Liu +1

Let $A$ be a symmetrizable generalized Cartan matrix with corresponding Kac--Moody algebra $g$ over $Q$ . Let $V = V^{λ}$ be an integrable highest weight $g$ -mod…

math.RT2022★ 1 cited

Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups

Dongwen Liu, Jia-Jun Ma, Fang Shi

In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi model for Deligne-Lusztig characters of finite symplectic groups, unitary groups, and general linear g…

math.RT2022★ 2 cited

Arithmetic Wavefront Sets and Generic $L$ -packets

Dihua Jiang, Dongwen Liu, Lei Zhang

Let $G$ be a classical group defined over a local field $F$ of characteristic zero. Let $π$ be an irreducible admissible representation $π$ of $G (F)$ , which is of Casselman-Wallach…

math.RT2021

Rankin-Selberg integrals for principal series representations of GL(n)

Dongwen Liu, Feng Su, Binyong Sun

We prove that the local Rankin--Selberg integrals for principal series representations of the general linear groups agree with certain simple integrals over the Rankin--Selberg sub…

math.RT2021

Rankin-Selberg convolutions for $GL (n) \times GL (n)$ and $GL (n) \times GL (n - 1)$ for principal series representations

Jian-Shu Li, Dongwen Liu, Feng Su +1

Let $k$ be a local field. Let $I_{ν}$ and $I_{ν^{'}}$ be smooth principal series representations of $GL_{n} (k)$ and $GL_{n - 1} (k)$ respectively. T…

math.RT2019★ 2 cited

Character expansion of Kac-Moody correction factors

Kyu-Hwan Lee, Dongwen Liu, Thomas Oliver

A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlyin…

math.RT2019★ 3 cited

On the Gan-Gross-Prasad problem for finite unitary groups

Dongwen Liu, Zhicheng Wang

In this paper we study the Gan-Gross-Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the exp…

math.RT2019★ 3 cited

Descents of unipotent cuspidal representations of finite classical groups

Dongwen Liu, Zhicheng Wang

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent cuspidal representations of orthogonal an…

math.RT2019★ 1 cited

Descents of unipotent representations of finite unitary groups

Dongwen Liu, Zhicheng Wang

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent representations of unitary groups over fi…

math.RT2019★ 7 cited

Remarks on the theta correspondence over finite fields

Dongwen Liu, Zhicheng Wang

S.-Y. Pan decomposes the uniform projection of the Weil representation of a finite symplectic-odd orthogonal dual pair, in terms of Deligne-Lusztig virtual characters, assuming tha…

math.RT2018

Theta lifting for loop groups

Dongwen Liu, Yongchang Zhu

In this paper we study the theta lifting for loop groups and extend the classical tower property established by S. Rallis to the loop setting. As an application we obtain cusp form…

math.RT2018★ 3 cited

Infinite dimensional Chevalley groups and Kac-Moody groups over $Z$

Lisa Carbone, Dongwen Liu, Scott H. Murray

Let $A$ be a symmetrizable generalized Cartan matrix, which is not of finite or affine type. Let $g$ be the corresponding Kac-Moody algebra over a commutative ring $R$ w…

math.RT2017★ 1 cited

LCA(2), Weil index, and product formula

Dongwen Liu, Yongchang Zhu

In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product fo…

math.RT2016

Archimedean zeta integrals on U(n,1)

Bingchen Lin, Dongwen Liu

For a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L-functions. In this pape…

math.RT2015★ 2 cited

Archimedean zeta integrals on U(2,1)

Dongwen Liu

It is known that for a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L-functi…

math.RT2013★ 2 cited

Eisenstein series on rank 2 hyperbolic Kac--Moody groups

Lisa Carbone, Kyu-Hwan Lee, Dongwen Liu

We define Eisenstein series on rank 2 hyperbolic Kac--Moody groups over R, induced from quasi--characters. We prove convergence of the constant term and hence the almost everywhere…

math.RT2011★ 294 cited

Theta functions and arithmetic quotients of loop groups

Dongwen Liu

In this paper we observe that isomorphism classes of certain metrized vector bundles over P^1-{0,infinity} can be parameterized by arithmetic quotients of loop groups. We construct…

Rankin--Selberg integrals of opposite conductor--one newforms

Betti-Whittaker periods of the contragredient representations for GL(n)

Fourier positivity for spherical functions I: split tori and spherical principal series

Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character

Archimedean period relations for Rankin-Selberg convolutions

Irreducible representations of GLn​(C) of minimal Gelfand-Kirillov dimension

Arithmetic Branching Law and generic L-packets

Strong integrality of inversion subgroups of Kac-Moody groups

Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups

Arithmetic Wavefront Sets and Generic L-packets

Rankin-Selberg integrals for principal series representations of GL(n)

Rankin-Selberg convolutions for GL(n)×GL(n) and GL(n)×GL(n−1) for principal series representations

Character expansion of Kac-Moody correction factors

On the Gan-Gross-Prasad problem for finite unitary groups

Descents of unipotent cuspidal representations of finite classical groups

Descents of unipotent representations of finite unitary groups

Remarks on the theta correspondence over finite fields

Theta lifting for loop groups

Infinite dimensional Chevalley groups and Kac-Moody groups over Z

LCA(2), Weil index, and product formula

Archimedean zeta integrals on U(n,1)

Archimedean zeta integrals on U(2,1)

Eisenstein series on rank 2 hyperbolic Kac--Moody groups

Theta functions and arithmetic quotients of loop groups

Betti-Whittaker periods of the contragredient representations for $GL (n)$

Irreducible representations of $GL_{n} (C)$ of minimal Gelfand-Kirillov dimension

Arithmetic Branching Law and generic $L$ -packets

Arithmetic Wavefront Sets and Generic $L$ -packets

Rankin-Selberg convolutions for $GL (n) \times GL (n)$ and $GL (n) \times GL (n - 1)$ for principal series representations

Infinite dimensional Chevalley groups and Kac-Moody groups over $Z$