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Chenyan Wu

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math.NT Computation and Language math.AG math.RT

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preprint2026arXiv

Associated Representations of finite pattern groups

In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first, we are able to classify the irreducible representations of the unipotent radical of the standard parabolic subgroups of $\mathrm{GL}_n$ with 4 parts; second, we can parameterize irreducible characters of degree $q$ in terms of coadjoint orbits of cardinality $q^2$ , for any finite pattern groups $G$ over $\mathbb{F}_q,$ where $\mathbb{F}_q$ is a finite field with $q$ elements.

preprint2026arXiv

DPN-LE: Dual Personality Neuron Localization and Editing for Large Language Models

With the widespread adoption of large language models (LLMs), understanding their personality representation mechanisms has become critical. As a novel paradigm in Personality Editing, most existing methods employ neuron-editing to locate and modify LLM neurons, requiring changes to numerous neurons and leading to significant performance degradation. This raises a fundamental question: Are all modified neurons directly related to personality representation? In this work, we investigate and quantify this specificity through assessments of general capability impact and representation-level patterns. We find that: 1) Current methods can change personalities but reduce overall performance. 2) Neurons are multifunctional, connecting personality traits and general knowledge. 3) Opposing personality traits demonstrate distinctly mutually exclusive representation patterns. Motivated by these findings, we propose DPN-LE (Dual Personality Neuron Localization and Editing), which identifies personality-specific neurons by contrasting MLP activations between high-trait and low-trait samples. DPN-LE constructs layer-wise steering vectors and applies dual-criterion filtering based on Cohen's $d$ effect size and activation magnitude to isolate mutually exclusive neuron subsets. Sparse linear intervention on these neurons enables precise personality control at inference time. Using only 1,000 contrastive sample pairs per trait, DPN-LE intervenes on $\sim$ 0.5\% of neurons while achieving competitive personality control and substantially better capability preservation across reasoning tasks. Experiments on LLaMA-3-8B-Instruct and Qwen2.5-7B-Instruct demonstrate the effectiveness and generalizability of our approach.

preprint2022arXiv

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Metaplectic Groups

We give constraints on the existence of $(χ,b)$ -factors in the global $A$ -parameter of a genuine cuspidal automorphic representation $σ$ of a metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to odd orthogonal groups. We also give a refined result that relates the invariant, first occurrence index, to non-vanishing of period integrals of residues of Eisenstein series associated to the cuspidal datum $χ\otimesσ$ . This complements our previous results for symplectic groups.

preprint2022arXiv

Poles of Eisenstein series and theta lifts for unitary groups

We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum $χ\otimesσ$ and the lowest occurrence of theta lifts of a cuspidal automorphic representation $σ$ of a unitary group, where $χ$ is a conjugate self-dual character. A key ingredient of the proof is the computation of period integrals of truncated Eisenstein series.

preprint2022arXiv

Virtual Abelian varieties of $\mathrm{GL}_2$ -type

This paper studies a class of Abelian varieties that are of $\GL_2$-type and with isogenous classes defined over a number field $k$ . We treat the cases when their endomorphism algebras are either (1) a totally real field $K$ or (2) a totally indefinite quaternion algebra over a totally real field $K$ . Among the isogenous class of such an Abelian variety, we identify one whose Galois conjugates can be described in terms of actions of Atkin-Lehner operators and the class group of $K$ . Thus we deduce that such Abelian varieties are parametrised by finite quotients of certain PEL Shimura varieties. These new families of moduli spaces are further analysed when they are of dimension $2$ . We provide explicit numerical bounds for when they are surfaces of general type. In addition, for two particular examples, we show that they are both rational surfaces by computing the coordinates of inequivalent elliptic points and studying the intersections of Hirzebruch cycles with exceptional divisors.

preprint2017arXiv

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Symplectic Groups

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $σ$ of symplectic groups $\mathrm{Sp}_{2n}(\mathbb{A})$ , which detects the right-most pole of the $L$ -function $L(s,σ\timesχ)$ for some character $χ$ of $F^\times\backslash\mathbb{A}^\times$ of order at most $2$ , and hence the occurrence of a simple global Arthur parameter $(χ,b)$ in the global Arthur parameter $ψ$ attached to $σ$ . We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.

preprint2016arXiv

On a Critical Case of Rallis Inner Product Formula

Let $π$ be a genuine cuspidal representation of the metaplectic group of rank $n$ . We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension $2n+1$ . We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands $L$ -function of $π$ twisted by a character. The bulk of this article focuses on proving a case of regularised Siegel-Weil formula, on which the Rallis inner product formula is based and whose proof is missing in the literature.

preprint2014arXiv

Irreducibility of Theta Lifting for Unitary Groups

This article shows that for unitary dual reductive pairs the first occurrence of theta lift of an irreducible cuspidal automorphic representation is irreducible. It also proves a refined tower property for theta lifts and the involutive property for twisted theta lifts.

preprint2014arXiv

On $(χ,b)$ -factors of Cuspidal Automorphic Representations of Unitary Groups I

Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations $σ$ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter $(χ,b)$ in the global Arthur parameter $ψ_σ$ associated to $σ$ , by the endoscopic classification of Arthur ([Art13], [Mok13], [KMSW14]). The argument uses the theory of theta correspondence. This can be viewed as a part of the $(χ,b)$ -theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain $L$ -functions, which was outlined in [Ral91].

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Chenyan Wu

Research overview

Is this your work?

9 publications

Associated Representations of finite pattern groups

DPN-LE: Dual Personality Neuron Localization and Editing for Large Language Models

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Metaplectic Groups

Poles of Eisenstein series and theta lifts for unitary groups

Virtual Abelian varieties of $\mathrm{GL}_2$ -type

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Symplectic Groups

On a Critical Case of Rallis Inner Product Formula

Irreducibility of Theta Lifting for Unitary Groups

On $(χ,b)$ -factors of Cuspidal Automorphic Representations of Unitary Groups I

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Chenyan Wu

Research overview

Is this your work?

9 publications

Associated Representations of finite pattern groups

DPN-LE: Dual Personality Neuron Localization and Editing for Large Language Models

Periods and (χ,b)(χ,b)(χ,b)-factors of Cuspidal Automorphic Forms of Metaplectic Groups

Poles of Eisenstein series and theta lifts for unitary groups

Virtual Abelian varieties of GL2\mathrm{GL}_2GL2​-type

Periods and (χ,b)(χ,b)(χ,b)-factors of Cuspidal Automorphic Forms of Symplectic Groups

On a Critical Case of Rallis Inner Product Formula

Irreducibility of Theta Lifting for Unitary Groups

On (χ,b)(χ,b)(χ,b)-factors of Cuspidal Automorphic Representations of Unitary Groups I

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Building this map preview

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Metaplectic Groups

Virtual Abelian varieties of $\mathrm{GL}_2$ -type

Periods and $(χ,b)$ -factors of Cuspidal Automorphic Forms of Symplectic Groups

On $(χ,b)$ -factors of Cuspidal Automorphic Representations of Unitary Groups I