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Huafeng Zhang

Publications and source records attributed to Huafeng Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Unitriangular R-matrices of quantum affine algebras and Yangians via Theta series

The universal R-matrix of the quantum affine algebra associated to a finite-dimensional simple complex Lie algebra admits a Gauss decomposition into an uper unitriangular part, an abelian part, and a lower unitriangular part. In this paper, we provide a simple conjugation formula for the unitriangular R-matrices with one tensor factor evaluated at an arbitrary finite-dimensional representation of the quantum affine algebra. Our formula involves the T-series of Frenkel--Hernandez and the Theta series introduced in a previous work. We also extend our conjugation formula to the Yangian case, making use of associators for triple tensor product representations of shifted Yangians.

math.QA↗
arXiv2025

An empirical formulation of accelerated molecular dynamics for simulating and predicting microstructure evolution in materials

Despite its widespread use in materials science, conventional molecular dynamics (MD) simulations are severely constrained by timescale limitations. To address this shortcoming, we propose an empirical formulation of accelerated MD method, adapted from a collective-variable-based extended system dynamics framework. While this framework is originally developed for efficient free energy sampling and reaction pathway determination of specific rare events in condensed matter, we have modified it to enable accelerated MD simulation and prediction of microstructure evolution of materials across a broad range of scenarios. In essence, the nearest neighbor off-centering absolute displacement (NNOAD), which quantifies the deviation of an atom from the geometric center of its nearest neighbors in materials, is introduced. We propose that the collection of NNOADs of all atoms can serve as a generalized reaction coordinate for various structural transitions in materials. The NNOAD of each atom, represented by its three components, is coupled with three additional dynamic variables assigned to the atom. Time evolution of the additional dynamic variables follows Langevin equation, while Nos\'e-Hoover dynamics is employed to thermostat the system. Through careful analysis and benchmark simulations, we established appropriate parameter ranges for the equations in our method. Application of this method to several test cases demonstrates its capability to accelerate MD simulations by several orders of magnitude while maintaining kinetic consistency and good accuracy in predicting long timescale microstructure evolutions of materials. We also provide some preliminary thoughts on theoretical justification of the method, offering insights into its underlying principles.

cond-mat.mtrl-sci↗
arXiv2025

AgentDAO: Synthesis of Proposal Transactions Via Abstract DAO Semantics

While the trend of decentralized governance is obvious (cryptocurrencies and blockchains are widely adopted by multiple sovereign countries), initiating governance proposals within Decentralized Autonomous Organizations (DAOs) is still challenging, i.e., it requires providing a low-level transaction payload, therefore posing significant barriers to broad community participation. To address these challenges, we propose a multi-agent system powered by Large Language Models with a novel Label-Centric Retrieval algorithm to automate the translation from natural language inputs into executable proposal transactions. The system incorporates DAOLang, a Domain-Specific Language to simplify the specification of various governance proposals. The key optimization achieved by DAOLang is a semantic-aware abstraction of user input that reliably secures proposal generation with a low level of token demand. A preliminary evaluation on real-world applications reflects the potential of DAOLang in terms of generating complicated types of proposals with existing foundation models, e.g. GPT-4o.

cs.SE↗
arXiv2025

Jordan-Hölder property for shifted quantum affine algebras

We prove that finite length representations of shifted quantum affine algebras in category $\mathcal{O}^{\mathrm{sh}}$ are stable by fusion product. This implies that in the topological Grothendieck ring $K_0(\mathcal{O}^{\mathrm{sh}})$ the Grothendieck group of finite length representations forms a non-topological subring. We also conjecture this subring is isomorphic to the cluster algebra discovered in arXiv:2401.04616. In the course of our proofs, we establish that any simple representation in category $\mathcal{O}^{\mathrm{sh}}$ descends to a truncation, for certain truncation parameters as conjectured in arXiv:2010.06996 in terms of Langlands dual $q$-characters.

math.QA↗
arXiv2024

Theta series for quantum loop algebras and Yangians

We introduce and study a family of power series, which we call Theta series, whose coefficients are in the tensor square of a quantum loop algebra. They arise from a coproduct factorization of the T-series of Frenkel--Hernandez, which are leading terms of transfer matrices of certain infinite-dimensional irreducible modules over the upper Borel subalgebra in the category O of Hernandez--Jimbo. We prove that each weight component of a Theta series is polynomial. As applications, we establish a decomposition formula and a polynomiality result for R-matrices between an irreducible module and a finite-dimensional irreducible module in category O. We extend T-series and Theta series to Yangians by solving difference equations determined by the truncation series of Gerasimov--Kharchev--Lebedev--Oblezin. We prove polynomiality of Theta series by interpreting them as associators for triple tensor product modules over shifted Yangians.

math.QA↗
arXiv2022

Shifted Yangians and polynomial R-matrices

We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by the representation theory of the Borel subalgebra of a quantum affine algebra and by the relevance of quantum integrable systems in this context, we prove that tensor products of prefundamental modules with irreducible modules are either cyclic or co-cyclic. This implies the existence and uniqueness of morphisms, the R-matrices, for such tensor products. We prove the R-matrices are polynomial in the spectral parameter, and we establish functional relations for the R-matrices. As applications, we prove the Jordan--Hölder property in the category O. We also obtain a proof, uniform for any finite type, that any irreducible module factorizes through a truncated shifted Yangian.

math.QA↗
arXiv2021

Industry Practice of Coverage-Guided Enterprise-Level DBMS Fuzzing

As an infrastructure for data persistence and analysis, Database Management Systems (DBMSs) are the cornerstones of modern enterprise software. To improve their correctness, the industry has been applying blackbox fuzzing for decades. Recently, the research community achieved impressive fuzzing gains using coverage guidance. However, due to the complexity and distributed nature of enterprise-level DBMSs, seldom are these researches applied to the industry. In this paper, we apply coverage-guided fuzzing to enterprise-level DBMSs from Huawei and Bloomberg LP. In our practice of testing GaussDB and Comdb2, we found major challenges in all three testing stages. The challenges are collecting precise coverage, optimizing fuzzing performance, and analyzing root causes. In search of a general method to overcome these challenges, we propose Ratel, a coverage-guided fuzzer for enterprise-level DBMSs. With its industry-oriented design, Ratel improves the feedback precision, enhances the robustness of input generation, and performs an on-line investigation on the root cause of bugs. As a result, Ratel outperformed other fuzzers in terms of coverage and bugs. Compared to industrial black box fuzzers SQLsmith and SQLancer, as well as coverage-guided academic fuzzer Squirrel, Ratel covered 38.38%, 106.14%, 583.05% more basic blocks than the best results of other three fuzzers in GaussDB, PostgreSQL, and Comdb2, respectively. More importantly, Ratel has discovered 32, 42, and 5 unknown bugs in GaussDB, Comdb2, and PostgreSQL.

cs.SE↗
arXiv2021

IntelliGen: Automatic Driver Synthesis for FuzzTesting

Fuzzing is a technique widely used in vulnerability detection. The process usually involves writing effective fuzz driver programs, which, when done manually, can be extremely labor intensive. Previous attempts at automation leave much to be desired, in either degree of automation or quality of output. In this paper, we propose IntelliGen, a framework that constructs valid fuzz drivers automatically. First, IntelliGen determines a set of entry functions and evaluates their respective chance of exhibiting a vulnerability. Then, IntelliGen generates fuzz drivers for the entry functions through hierarchical parameter replacement and type inference. We implemented IntelliGen and evaluated its effectiveness on real-world programs selected from the Android Open-Source Project, Google's fuzzer-test-suite and industrial collaborators. IntelliGen covered on average 1.08X-2.03X more basic blocks and 1.36X-2.06X more paths over state-of-the-art fuzz driver synthesizers FUDGE and FuzzGen. IntelliGen performed on par with manually written drivers and found 10 more bugs.

cs.SE↗
arXiv2020

Yangians and Baxter's relations

We study a category O of representations of the Yangian associated to an arbitrary finite-dimensional complex simple Lie algebra. We obtain asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov--Reshetikhin modules. In the Grothendieck ring we establish the three-term Baxter's TQ relations for the asymptotic modules. We indicate that Hernandez--Jimbo's limit construction can also be applied, resulting in modules over anti-dominantly shifted Yangians.

math.QA↗
arXiv2018

Elliptic quantum groups and Baxter relations

We introduce a category O of modules over the elliptic quantum group of sl_N with well-behaved q-character theory. We construct asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov--Reshetikhin modules. In the Grothendieck ring of this category we prove two types of identities: generalized Baxter relations in the spirit of Frenkel--Hernandez between finite-dimensional modules and asymptotic modules; three-term Baxter TQ relations of infinite-dimensional modules.

math-ph↗
arXiv2017

Length-two representations of quantum affine superalgebras and Baxter operators

Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations; the extended T-systems of Kirillov--Reshetikhin modules. We make use of these representations over the full quantum affine superalgebra to define Baxter operators as transfer matrices for the quantum integrable model and to deduce Bethe Ansatz Equations, under genericity conditions.

math-ph↗
arXiv2017

Asymptotic Representations of Quantum Affine Superalgebras

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called $q$-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.

math.QA↗
arXiv2016

RTT realization of quantum affine superalgebras and tensor products

We use the RTT realization of the quantum affine superalgebra associated with the Lie superalgebra $\mathfrak{gl}(M,N)$ to study its finite-dimensional representations and their tensor products. In the case $\mathfrak{gl}(1,1)$, the cyclicity condition of tensor products of finite-dimensional simple modules is determined completely in terms of zeros and poles of rational functions. This in turn induces cyclicity of some particular tensor products of Kirillov-Reshetikhin modules related to $\mathfrak{gl}(M,N)$.

math.QA↗
arXiv2016

Baxter operators and asymptotic representations

We introduce a category $\mathcal O$ of representations of the elliptic quantum group associated with $\mathfrak{sl}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in the Grothendieck ring of this category. Baxter $Q$-operators are obtained as transfer matrices for asymptotic representations and obey $TQ$-relations as a consequence of the relations in $K_0(\mathcal O)$.

math.QA↗
arXiv2016

Fundamental representations of quantum affine superalgebras and R-matrices

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices between two fundamental representations are computed; a cyclicity (and so simplicity) condition on tensor products of fundamental representations is proved.

math.QA↗
arXiv2015

Universal R-matrix of quantum affine gl(1,1)

The universal $R$-matrix of the quantum affine superalgebra associated to the Lie superalgebra $\mathfrak{gl}(1,1)$ is realized as the Casimir element of certain Hopf pairing, based on the explicit coproduct formula of all the Drinfeld loop generators.

math.QA↗
arXiv2014

Representations of Quantum Affine Superalgebras

We study the quantum affine superalgebra $U_q(Lsl(M,N))$ and its finite-dimensional representations. We prove a triangular decomposition and establish a system of Poincaré-Birkhoff-Witt generators for this superalgebra, both in terms of Drinfel'd currents. We define the Weyl modules in the spirit of Chari-Pressley and prove that these Weyl modules are always finite-dimensional and non-zero. In consequence, we obtain a highest weight classification of finite-dimensional simple representations when $M \neq N$. Some concrete simple representations are constructed via evaluation morphisms.

math.QA↗