arXiv subjects

Fulin Chen

Publications and source records attributed to Fulin Chen.

At least 19 recordsLinked to original sources

arXiv2026

HybridFlow: A 2-NFE Generative Policy for Real-Time Robotic Manipulation

Generative policies for robotic manipulation must balance action accuracy with inference latency. We present HybridFlow, a three-stage policy inference procedure requiring two network function evaluations (2-NFE). A Global Jump uses the MeanFlow average velocity to generate a coarse action trajectory; a parameter-free ReNoise interpolation constructs a state at a nonzero refinement time; and a Local Refine queries the instantaneous-velocity limit of the same network at that time. This construction reuses a unified model without distillation. Our analysis characterizes interval-composition errors and the attenuation of endpoint error under ReNoise interpolation. Controlled RoboMimic ablations support the MeanFlow proposal and intermediate-state construction, achieving 95% average success with reused noise and 95.5% with fresh noise, versus 78% for one-step MeanFlow. Across five real-robot settings with all policies running on the same Jetson AGX Thor, HybridFlow improves normalized task performance over 16-step Diffusion Policy by 13-68 points with approximately eightfold lower action-generation latency. Additional experiments demonstrate its compatibility as an action expert in a vision-language-action framework. Project page: https://hybridflow-anonymous.pages.dev/

cs.RO↗

arXiv2026

Shared Execution-Clock Drifting Policy for Dynamic Precision Manipulation

Manipulation under time constraints requires both accurate actions and an execution rhythm that matches the evolving scene. This becomes critical when a robot must intercept moving objects or complete a sequence of adjustments before a deadline. Although one-step policies reduce generation cost, their directly predicted action sequences leave temporal allocation implicit. We propose Shared Execution-Clock Drifting (SECD), which makes execution rhythm an explicit part of one-step action generation. Conditioned on an observation and a latent sample, the policy jointly predicts a progress-indexed action curve and a shared monotone clock that maps fixed control times to locations on the curve. Demonstration-derived alignment anchors this decomposition, which is trained jointly through drifting on the decoded actions. The resulting policy retains a fixed-rate control interface and requires one network evaluation. We evaluate SECD across four real-robot tasks with inference on NVIDIA Thor. Across 300 trials, it achieves 77.00% task-averaged success and outperforms the evaluated one-step baselines on every task, including 91% success in cup retrieval from a 16 m/min conveyor and 54% in restoring and folding a crumpled shirt within 90 s. A fixed-clock variant reaches 79% on the same conveyor protocol. Complementary state-based RoboMimic experiments, including cross-seed ablations on Transport and Square, further support the joint design of the temporal representation and demonstration alignment. Project page: https://secd-anonymous-ewn.pages.dev/

cs.RO↗

arXiv2026

Representations of formal Lie groups and Lie pairs

Formal Lie groups, which generalize Lie groups in differential geometry, are analogous to formal group schemes in algebraic geometry. In a previous paper, we established the basic theory of formal Lie groups, including a formal Lie theory theorem that identifies formal Lie groups with Lie pairs. In this paper, we develop the foundations of the representation theory of formal Lie groups and Lie pairs. In particular, we construct modules of Lie pairs on function spaces over formal manifolds and prove that the category of representations of a formal Lie group is isomorphic to the category of modules of the corresponding Lie pair.

math.RT↗

arXiv2026

Almost multiplicity-one property of spherical varieties over finite fields

Let $H$ be a connected algebraic subgroup of a connected reductive group $G$ over a finite field $\mathbb F_q$ such that $G/H$ is a $G$-spherical variety, i.e., $G/H$ has an open dense $B$-orbit for each Borel subgroup $B$ of $G$. We formulate, for the pair $(G,H)$, an almost multiplicity-one property. Then we establish a criterion for this property in terms of the $B$-stabilizers on $G/H$. In particular, we will see that this property is analogous to the strongly tempered condition in characteristic $0$.

math.RT↗

arXiv2026

Local Weyl modules and skew Howe duality

The skew $(\mathfrak{gl}_{n}, \mathfrak{gl}_{r})$ Howe duality states that the exterior algebra $Λ(\mathbb{C}^{nr})$ admits a multiplicity-free decomposition under the natural actions of $\mathfrak{gl}_{n}\times \mathfrak{gl}_{r}$. In this paper, by using certain Lagrange interpolation polynomials of degree $r-1$, we extend the action of $\mathfrak{gl}_{n}$ on $Λ(\C^{nr})$ to its loop algebra $L(\mathfrak{gl}_{n})$. View $Λ(\C^{nr})$ as a module for the loop algebra $L(\mathfrak{sl}_{n})$ of $\mathfrak{sl}_{n}$ by taking restriction. We prove that every highest weight vector of $\mathfrak{gl}_{n}\times \mathfrak{gl}_{r}$ in $Λ(\C^{nr})$ generates a local Weyl module of $L(\mathfrak{sl}_{n})$. Furthermore, we obtain in this way an explicit realization of all local Weyl modules for $L(\mathfrak{sl}_{n})$.

math.RT↗

arXiv2026

Lie pairs and formal Lie groups

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular, extending the classical formal Lie theory theorem, we prove that the category of formal Lie groups is equivalent to the category of Lie pairs.

math.RT↗

arXiv2026

FAR-Dex: Few-shot Data Augmentation and Adaptive Residual Policy Refinement for Dexterous Manipulation

Achieving human-like dexterous manipulation through the collaboration of multi-fingered hands with robotic arms remains a longstanding challenge in robotics, primarily due to the scarcity of high-quality demonstrations and the complexity of high-dimensional action spaces. To address these challenges, we propose FAR-Dex, a hierarchical framework that integrates few-shot data augmentation with adaptive residual refinement to enable robust and precise arm-hand coordination in dexterous tasks. First, FAR-DexGen leverages the IsaacLab simulator to generate diverse and physically constrained trajectories from a few demonstrations, providing a data foundation for policy training. Second, FAR-DexRes introduces an adaptive residual module that refines policies by combining multi-step trajectory segments with observation features, thereby enhancing accuracy and robustness in manipulation scenarios. Experiments in both simulation and real-world demonstrate that FAR-Dex improves data quality by 13.4% and task success rates by 7% over state-of-the-art methods. It further achieves over 80% success in real-world tasks, enabling fine-grained dexterous manipulation with strong positional generalization.

cs.RO↗

arXiv2026

Vector-valued Gelfand-Kazhdan criterion

The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual Gelfand-Kazhdan criterion, we formulate and prove a vector-valued Gelfand-Kazhdan criterion that fits into the general framework of the relative Langlands program. As an illustration of its effectiveness, we establish the multiplicity-one property for the local Asai Rankin-Selberg periods.

math.RT↗

arXiv2025

Non-weight modules over gap-$p$ Virasoro algebras

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 and irreducible restricted modules is also determined.

math.RT↗

arXiv2025

Formal manifolds: local structure of morphisms, and formal submanifolds

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study their basic theory, focusing on function spaces and Poincare's lemma. In this paper, we further explore the foundational framework of formal manifolds, including the local structure of constant rank morphisms (such as inverse function theorem and constant rank theorems) as well as the theory of formal submanifolds.

math.DG↗

arXiv2024

Poincaré's lemma for formal manifolds

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds, including generalizations of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. In this paper, we establish Poincaré's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.

math.FA↗

arXiv2024

Formal manifolds: foundations

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of formal manifolds in the context of differential geometry, inspired by the notion of formal schemes in algebraic geometry. We develop the basic theory for formal manifolds, and establish a fully faithful contravariant functor from the category of formal manifolds to the category of topological $\mathbb{C}$-algebras. We also prove the existence of finite products in the category of formal manifolds by studying vector-valued formal functions.

math.DG↗

arXiv2024

Function spaces on formal manifolds

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the foundational framework of formal manifolds. In this paper, we study various function spaces on formal manifolds, including generalizations of vector-valued generalized functions and vector-valued distributions on smooth manifolds to the setting of formal manifolds.

math.FA↗

arXiv2024

Quantum vertex algebra associated to quantum toroidal $\mathfrak{gl}_N$

In this paper, we associate the quantum toroidal algebra $\mathcal{E}_N$ of type $\mathfrak{gl}_N$ with quantum vertex algebra through equivariant $ϕ$-coordinated quasi modules. More precisely, for every $\ell\in \mathbb{C}$, by deforming the universal affine vertex algebra of $\mathfrak{sl}_\infty$, we construct an $\hbar$-adic quantum $\Z$-vertex algebra $V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$. Then we prove that the category of restricted $\mathcal{E}_N$-modules of level $\ell$ is canonically isomorphic to that of equivariant $ϕ$-coordinated quasi $V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$-modules.

math.QA↗

arXiv2023

Howe duality in the toroidal setting

In this paper, we construct and study various dual pairs acting on the oscillator modules of the symplectic toroidal Lie algebras coordinated by irrational quantum tori. This extends the classical Howe dual pairs to the toroidal setup.

math.QA↗

arXiv2023

Vertex algebras and TKK algebras

In this paper, we associate the TKK algebra $\widehat{\mathcal{G}}(\mathcal{J})$ with vertex algebras through twisted modules. Firstly, we prove that for any complex number $\ell$, the category of restricted $\widehat{\mathcal{G}}(\mathcal{J})$-modules of level $\ell$ is canonically isomorphic to the category of $σ$-twisted $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$-modules, where $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ is a vertex algebra arising from the toroidal Lie algebra of type $C_2$ and $σ$ is an isomorphism of $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ induced from the involution of this toroidal Lie algebra. Secondly, we prove that for any nonnegative integer $\ell$, the integrable restricted $\widehat{\mathcal{G}}(\mathcal{J})$-modules of level $\ell$ are exactly the $σ$-twisted modules for the quotient vertex algebra $L_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ of $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$. Finally, we classify the irreducible $\frac{1}{2}{\mathbb{N}}$-graded $σ$-twisted $L_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$-modules.

math.QA↗

arXiv2022

A unified construction of vertex algebras from infinite-dimensional Lie algebras

In this paper, we give a unified construction of vertex algebras arising from infinite-dimensional Lie algebras, including the affine Kac-Moody algebras, Virasoro algebras, Heisenberg algebras and their higher rank analogs, orbifolds and deformations. We define a notion of what we call quasi vertex Lie algebra to unify these Lie algebras. Starting from any (maximal) quasi vertex Lie algebra $\mathfrak{g}$, we construct a corresponding vertex Lie algebra ${\mathfrak{g}}_0$, and establish a canonical isomorphism between the category of restricted $\mathfrak{g}$-modules and that of equivariant $ϕ$-coordinated quasi $V_{\mathfrak{g}_0}$-modules, where $V_{\mathfrak{g}_0}$ is the universal enveloping vertex algebra of ${\mathfrak{g}}_0$. This unified all the previous constructions of vertex algebras from infinite-dimensional Lie algebras and shed light on the way to associate vertex algebras with Lie algebras.

math.QA↗

arXiv2022

Twisted quantum affinizations and quantization of extended affine Lie algebras

In this paper, for an arbitrary Kac-Moody Lie algebra $\mathfrak g$ and a diagram automorphism $μ$ of $\mathfrak g$ satisfying certain natural linking conditions, we introduce and study a $μ$-twisted quantum affinization algebra $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$ of $\mathfrak g$. When $\mathfrak g$ is of finite type, $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$ is Drinfeld's current algebra realization of the twisted quantum affine algebra. When $μ=\mathrm{id}$ and $\mathfrak g$ in affine type, $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$ is the quantum toroidal algebra introduced by Ginzburg, Kapranov and Vasserot. As the main results of this paper, we first prove a triangular decomposition for $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$. Second, we give a simple characterization of the affine quantum Serre relations on restricted $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$-modules in terms of "normal order products". Third, we prove that the category of restricted $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$-modules is a monoidal category and hence obtain a topological Hopf algebra structure on the "restricted completion" of $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$. Last, we study the classical limit of $\mathcal U_\hbar\left(\hat{\mathfrak g}_μ\right)$ and abridge it to the quantization theory of extended affine Lie algebras. In particular, based on a classification result of Allison-Berman-Pianzola, we obtain the $\hbar$-deformation of all nullity $2$ extended affine Lie algebras.

math.QA↗