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Chun-Hui Wang

Publications and source records attributed to Chun-Hui Wang.

14 recordsLinked to original sources
arXiv2026

Siegel modular forms associated to Weil representations: $\operatorname{SL}_2(\mathbb{R}) \& \operatorname{GL}_2(\mathbb{R})$ cases

We investigate explicit modular forms of weights $1/2$ and $3/2$-classical, minus, and fermionic theta series-arising from the classical Weil representation associated to $\operatorname{SL}_2(\mathbb{R})$ via the $2$-cocycles of Rao, Kudla, Perrin, Lion--Vergne and Satake--Takase. We reorganize these forms using (tensor) induction, and subsequently extend our study to the similitude group $\operatorname{GL}_2(\mathbb{R})$.

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arXiv2025

Siegel modular forms associated to Weil representations

We study some explicit Siegel modular forms from Weil representations. For the classical theta group $Γ_m(1,2)$ with $m > 1$, there are some eighth roots of unity associated with these modular forms, as noted in the works of Andrianov, Friedberg, Maloletkin, Stark, Styer, Richter, and others. We apply $2$-cocycles introduced by Rao, Kudla, Perrin, Lion-Vergne, Satake-Takase to investigate these unities. We extend our study to the full Siegel group $\operatorname{Sp}_{2m}(\mathbb{Z})$ and obtain two matrix-valued Siegel modular forms from Weil representations; these forms arise from a finite-dimensional representation $\operatorname{Ind}_{\widetildeΓ'_m(1,2)}^{\widetilde{\operatorname{Sp}}'_{2m}(\mathbb{Z})} (1_{Γ_m(1,2)} \cdot \operatorname{Id}_{μ_8})^{-1}$, which is related to Igusa's quotient group $\tfrac{\operatorname{Sp}_{2m}(\mathbb{Z})}{Γ_m(4,8)}$.

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arXiv2024

On the lattice model of the Weil representation

Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in another paper. We extend this family of representations to a representation of a Jacobi subgroup by incorporating a rational Metaplectic group. In the case of F being a non-archimedean local field of odd residual characteristic or a finite unramified extension of the field of 2-adic numbers, we obtain similar results for a Jacobi group by incorporating a Metaplectic group.

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arXiv2024

Extended Weil representations: the non-dyadic local field cases

Let F be a non-archimedean local field of odd residual characteristic. Let W be a symplectic vector space over F. It is known that there are different Weil representations of a Meteplectic covering group Mp(W). By some twisted actions, we reorganize them as a representation of $PGMp^{\pm}(W)$, which is a covering group related to the projective similitude symplectic group.

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arXiv2023

Extended Weil representations: the real field case

Let F be the usual real field. Let W be a symplectic vector space over F. It is known that there are two different Weil representations of a Meteplectic covering group $\widetilde{Sp}(W)$. By some twisted actions, we reorganize them into a representation of $\widetilde{Sp}^{\pm}(W)$, a covering group over a subgroup $Sp^{\pm}(W)$ of $GSp(W)$. Based on the works of MVW, Kudla, and Howe on reductive dual pairs in $Sp(W)$, we explore the analogous dual pairs in $Sp^{\pm}(W)$ . Finally, following Lion-Vergne's classical book on Weil representations and theta series, we investigate some simple theta series in $Sp^{\pm}(W)$ where $W$ has dimension two.

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arXiv2023

Extended Weil representations: the finite field cases

It is well known(cf. Weil, Gérardin's works) that there are two different Weil representations of a symplectic group over an odd finite field. By a twisted action, we show that one can reorganize them as a representation of a related projective symplectic similitude group. We also discuss the even field case by following Genestier-Lysenko and Gurevich-Hadani's works on geometric Weil representations in characteristic two. As a result, we approach some of their results from the lattice model, which is inspired by MVW, Prasad and Takeda's works.

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arXiv2021

Notes on unitary theta representations of compact groups

We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and restriction functors.

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arXiv2021

On the local theta representation

We study the algebraic framework in which one can define, in the manner of the theta correspondence, a correspondence between representations of two locally profinite groups $H_1$, $H_2$. In particular, we examine when and how such a correspondence can be extended to bigger groups $G_1$, $G_2$ containing $H_1$, $H_2$ respectively as normal subgroups. As an application, we discuss the theta correspondence for a reductive dual pair of the similitude groups in the non-archimedean case.

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arXiv2018

Splitting metaplectic cover groups

If $(G_1, G_2)$ is a dual reductive pair of type I in $Sp(W)$, it is known that the degree $8$ metaplectic cover of $Sp(W)$ splits over $G_1G_2$, with one obvious exception. In this paper we replace $G_1G_2$ by a larger subgroup obtained via similitude groups, and show that the degree $8$ metaplectic cover splits, with the same obvious exception.

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arXiv2013

On a question of Drinfeld on the Weil representation I: the finite field case

Let F be a finite field of odd cardinality, and let G= GL2(F). The group G \times G \times G acts on F^2 \otimes F^2 \otimes F^2 via symplectic similitudes, and has a natural Weil representation. Answering a question rasised by V. Drinfeld, we decompose that representation into irreducibles. We also decompose the analogous representation of GL2(A), where A is a cubic algebra over F.

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arXiv2013

Weil representations over finite fields and Shintani lift

Let Sp_V(F) be the group of isometries of a symplectic vector space V over a finite field F of odd cardinality. The group Sp_V(F) possesses distinguished representations--- the Weil representations. We know that they are compatible with base change in the sense of Shintani for a finite extension F'/F. The result is also true for the group of similitudes of V.

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