Cited by 286Geometric and Algebraic TopologyAlgebraic structures and combinatorial modelsBlack Holes and Theoretical Physics

The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index.

Gauge theories, vertex models, and quantum groups

Witten, Edward·1990·Nuclear Physics B

DOI 10.1016/0550-3213(90)90115-t

Open this paper in CoChat — free account

Integrity signals

Registry

Crossref · 10.1016/0550-3213(90)90115-t

Cites

28 of 28 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Phase Transitions and Critical Phenomena
Hoch, M. J. R. (2016) · CRC Press eBooks · doi:10.1201/9781439850541-13 · Cited by 11,466
Exactly Solved Models in Statistical Mechanics
Moore, M. A. (1983) · Physics Bulletin · doi:10.1088/0031-9112/34/4/045 · Cited by 4,876
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
Self-citation
Aq-difference analogue of U(g) and the Yang-Baxter equation
Jimbo, M. (1985) · Letters in Mathematical Physics · doi:10.1007/bf00704588 · Cited by 2,564
Current algebra and Wess-Zumino model in two dimensions
Knizhnik, V. G., & Zamolodchikov, A. B. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90374-2 · Cited by 1,781
A polynomial invariant for knots via von Neumann algebras
Jones, V. F. R. (1985) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1985-15304-2 · Cited by 1,641
Fusion rules and modular transformations in 2D conformal field theory
Verlinde, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90603-7 · Cited by 1,537
State models and the jones polynomial
Kauffman, L. H. (1987) · Topology · doi:10.1016/0040-9383(87)90009-7 · Cited by 1,465
Quantization of Lie Groups and Lie Algebras
Faddeev, L. D., Reshetikhin, N., & Takhtajan, L. A. (1988) · Elsevier eBooks · doi:10.1016/b978-0-12-400465-8.50019-5 · Cited by 1,189
Twisted $\textit{SU}(2)$ Group. An Example of a Non-Commutative Differential Calculus
Woronowicz, S. L. (1987) · Publications of the Research Institute for Mathematical Sciences · doi:10.2977/prims/1195176848 · Cited by 842

Show all 29 references

Research works printed but not linked: 9

V.G. Turaev, The Yang-Baxter equation and invariants of links, LOMI preprint
M. Rosso, Quantum groups and V. Jones' vertex models for knots, preprint
Belavin, 1987, Nucl. Phys., B281, 509
Classical And Quantum Conformal Field Theory, IAS preprint HEP-88/39, Nucl. Phys. B, to appear.
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Quantum group interpretation of some conformal field theories, preprint CERN-TH-5267/88.
D. Smit, Utrecht preprint (1989)
H. Au-Yang, B. McCoy, J.H. Perk and S. Tang, in Algebraic analysis, ed. M. Kashiwara and T. Kawai (Academic Press, New York);
T. Kohno, Quantized universal enveloping algebras and monodromy of braid groups, preprint
V. Pasquier, Continuum limit of lattice models built on quantum groups, Saclay preprint

Sorted by citations

Items 201–286 of 286

BFV--BRST Analysis of the Classical and Quantum q-deformations of the sl(2) AlgebraPreprint
Dayi, O. F., & International Centre for Theoretical Physics, T. (. (1993) · Cited by 3
Hochschild homology and cohomology of down–up algebras
Chouhy, S., Herscovich, E., & Solotar, A. (2017) · Journal of Algebra · doi:10.1016/j.jalgebra.2017.11.026 · Cited by 2
Photophysics of EGFP (E222H) Mutant, with Comparisons to Model Chromophores: Excited State pK’s, Progressions, Quenching and Exciton Interaction
Kirk, W. R., Allen, T., Atanasova, E. A., Wessels, W. S., Yao, J. Z., & Prendergast, F. G. (2017) · Journal of Fluorescence · doi:10.1007/s10895-017-2025-2 · Cited by 2
Nonlinear Commutation Relations: Representations by Point-Supported Operators
Karasev, M. V., & Novikova, E. M. (2002) · Mathematical Notes · doi:10.1023/a:1019865004455 · Cited by 2
(p,q)-deformed Virasoro-Witt n-algebraPreprint
Jia, X.-Y., Lu, D., Yan, Z., & Wang, S. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.07837 · Cited by 2
Integrability and quantum symmetries
Gómez, C., & Sierra, G. (1991) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(91)90127-z · Cited by 2
Search for minimal quantum group SUq(2) gauge field theory
Aref’eva, I. Y., & Arutyunov, G. E. (1993) · Journal of Geometry and Physics · doi:10.1016/0393-0440(93)90067-o · Cited by 2
Duality ensures modular covariance
Li, M., & Yu, M. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)91010-9 · Cited by 2
The quantized symmetries of N=2 superconformal field theories
Jiménez, F. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90289-3 · Cited by 2
Characters of theUq(sl(3,C)) Highest Weight Modules
Dobrev, V. K. (1990) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.102.137 · Cited by 2
Спиновые цепочки и дуальность между теорией струн и калибровочными теориями
Горский, А. С., & Gorsky, A. (2005) · Теоретическая и математическая физика · doi:10.4213/tmf1775 · Cited by 2
Black Horizons and Integrability in String TheoryPreprint
Fontanella, A. (2018) · arXiv (Cornell University) · doi:10.15126/thesis.00849271 · Cited by 2
Augmented down-up algebras and uniform posetsPreprint
Terwilliger, P., & Worawannotai, C. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1206.0455 · Cited by 2
Heisenberg double and Drinfeld double of the quantum superplanePreprint
Aghaei, N., & Pawelkiewicz, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.04565 · Cited by 2
1 General realization of N = 4 supersymmetric quantum mechanics and its applicationsPreprint
Ruan, D., & Huang, W. (2002) · Cited by 2
Single boson realizations of the deformed angular momentum algebra of Witten’s types
Huang, H., & Ruan, D. (2013) · Chinese Science Bulletin · doi:10.1007/s11434-013-5872-5 · Cited by 1
SINGLE BOSON AND INVERSION BOSON REALIZATIONS OF MULTI-PARAMETER NONLINEARLY DEFORMED ANGULAR MOMENTUM ALGEBRA
Ruan, D., Huang, H., & Li, Y. (2013) · Modern Physics Letters A · doi:10.1142/s0217732313501137 · Cited by 1
Indecomposable representations and boson realizations of the nonlinear deformed angular momentum algebra of Witten’s first type
Li, Y., Huang, H., & Ruan, D. (2012) · Journal of Mathematical Chemistry · doi:10.1007/s10910-012-0114-7 · Cited by 1
Deformations of quantum hyperplanes
Post, G. F. (1996) · Letters in Mathematical Physics · doi:10.1007/bf00714374 · Cited by 1
CONFORMAL $\mathcal{s}$$\mathcal{l}$2 ENVELOPING ALGEBRAS AS AMBISKEW POLYNOMIAL RINGS
O’Neill, M. (2002) · Proceedings of the Edinburgh Mathematical Society · doi:10.1017/s0013091500000419 · Cited by 1
On Category O over triangular generalized Weyl algebras
Khare, A., & Tikaradze, A. (2015) · Journal of Algebra · doi:10.1016/j.jalgebra.2015.11.035 · Cited by 1
Representation of Real Forms of Witten's First Deformation
Popovych, S., & Shevchenko, T. (1997) · Cited by 1
Composite link polynomials from super Chern-Simons theory
Backofen, O. J. (1996) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00044-5 · Cited by 1
Two Kinds of Two-Boson Realizations of Generally Deformed Algebras with Three Generators
Ruan, D., Li, Y., & Hongzhou, S. (2007) · Communications in Theoretical Physics · doi:10.1088/0253-6102/47/3/031 · Cited by 1
Composite A,B,C,D-IRF-model invariants
Backofen, O. J. (1996) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00027-5 · Cited by 1
General realization of N=4 supersymmetric quantum mechanics and its applications
Ruan, D., & Huang, W. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1578531 · Cited by 1
Braid group related algebras, their representations and generalized hydrogenlike spectra
Arık, M., Aydin, F., Hızel, E., Kornfilt, J., & Yildiz, A. K. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530506 · Cited by 1
Duality and modular invariance in rational conformal field theories
Li, M. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02100274 · Cited by 1
Quommutator deformations of spl(N,1)
Brihaye, Y. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532499 · Cited by 1
Polynomial equations and modular transformations in topological field theory
Chair, N., & Zhu, C.-J. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)90903-j · Cited by 1
BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra
Dayi, O. F. (1994) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/27/1/016 · Cited by 1
Quantum symmetries in the free field realization of Wn algebras
Cuerno, R. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90093-6 · Cited by 1
Нелинейные перестановочные соотношения: представления точечными операторами
Карасев, М. В., Karasev, M. V., & Novikova, E. M. (2002) · Математические заметки · doi:10.4213/mzm404 · Cited by 1
A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras.Preprint
Petersen, J. U. H. (1992) · Cited by 1
Characters of the Uq(sl(3, C)) Highest Weight Modules
Dobrev, V. K. (2013) · Progress of Theoretical Physics Supplement · doi:10.1143/ptp.102.137 · Cited by 1
The Superalgebra spl(p,q) and Differential Operators
Brihaye, Y., Giller, S., & Kosiński, P. (1998) · Acta Applicandae Mathematicae · doi:10.1023/a:1006083505435 · Cited by 1
Comments on rational conformal field theory, quantum groups and tower of algebras
Gómez, C. (2008) · Springer eBooks · doi:10.1007/3-540-53503-9_50
A note on vertex models and knot polynomials
Hayashi, M. (1990) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/23/19/006
Algebraic equations determining quantum dimensions
Hayashito, M. (1994) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/27/7/020
Cuntz deformations of the exterior algebra
Kehagias, A. (1993) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/26/19/011
From N=2 supergravity to constrained moduli spaces
Anselmi, D., Fré, P., Girardello, L., & Soriani, P. (1995) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(95)00438-f
A new relation among Catalan numbers
Nilsson, B. E. W., & Sundell, P. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531233
Dynamics with unitary phase operator: implications for Wigner's problem
Johal, R. S. (2002) · Physics Letters A · doi:10.1016/s0375-9601(01)00807-6
The second form of Delbecq and Quesne’s cubic deformation ofsu(2) and deformed Heisenberg-Weyl algebra
Chung, W.-S. (1995) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02741498
LIE ALGEBRAS: Infinite Generalizations and Deformations
Fletcher, P. T. (1990) · Durham e-Theses (Durham University)
Polynomial Realization of the Uq(sl(3)) Gel’Fand-(Weyl)-Zetlin Basis and Irregular Irreps at Roots of Unity
Dobrev, V. K., & Truini, P. (1998) · Springer eBooks · doi:10.1007/978-1-4899-1537-5_5
Regularity and K0-group of quadric solvable polynomial algebras
Li, H. (2003) · Journal of Algebra · doi:10.1016/s0021-8693(03)00149-2
ON THE CLASSICAL LIMIT OF THE GENERALIZED q-DEFORMED SU q(2) AND SU q(1,1) ALGEBRAS
Johal, R. S., GUPTA, R. K., & Sahai, V. (1998) · Modern Physics Letters A · doi:10.1142/s0217732398000139
Boson realizations of Fairlie's two-parameter deformedSU(2)
Fradkin, D. M. (1995) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02813598
Perturbative and non-perturbative aspects of Chern-Simons
Huang, H., & Maxim Zabzine, A. (2014)
The q-Deformed Cartesianosp(1/2) algebra
Chung, W.-S. (1995) · International Journal of Theoretical Physics · doi:10.1007/bf00674447
Junctions of refined Wilson lines and one-parameter deformation of quantum groupsPreprint
Chun, S. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1701.03518
Skew Derivations on Down-up Algebras
Almulhem, M., & Brzeziński, T. (2019) · Trends in mathematics · doi:10.1007/978-3-030-01156-7_7
THE DISCUSSION ON THE NORMAL FUNDAMENTAL REGION OF FUCHS GROUP WITH NONEUCLIDEAN GEOMETRY
Sun, Z. (1994) · Acta Mathematica Scientia · doi:10.1016/s0252-9602(18)30003-1
FROM N=2 SUPERGRAVITY TO CONSTRAINED MODULI SPACES
ANSELMI, D., P, F., L, G., & P., S. (1994) · CINECA IRIS Institutial research information system (University of Pisa)
Fermionic QFT, Grassmann calculus, and combinatorics
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0006
Combinatorial QFT and the Jacobian Conjecture
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0005
SYK-like tensor models
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0016
Quantum gravity, group field theory (GFT), and combinatorics
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0010
Algebraic combinatorics and QFT
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0008
Random tensor models—the multi-orientable (MO) model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0013
Quantum field theory (QFT)—built-in combinatorics
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0003
Tree weights and renormalization in QFT
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0004
QFT on the non-commutative Moyal space and combinatorics
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0009
Random tensor models—theU(N)D-invariant model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0012
Analytic combinatorics and QFT
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0007
Graphs, ribbon graphs, and polynomials
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0002
The Sachdev–Ye–Kitaev (SYK) holographic model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0015
From random matrices to random tensors
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0011
Generalized down-up algebras revisited from a viewpoint of Gröbner basis theory
Tuniyaz, R., & Yunus, G. (2022) · Communications in Algebra · doi:10.1080/00927872.2022.2032121
Extended chiral conformal theories with a quantum symmetry
Hadjiivanov, L. K., Paunov, R. R., & Todorov, I. T. (1992) · Lecture notes in mathematics · doi:10.1007/bfb0101195
Ideals of the Enveloping Algebra 𝑈(𝑠𝑙₃)
Catoiu, S. (2015) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/634/12690
Introduction
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0001
Random tensor models—theO(N)3-invariant model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.003.0014
Proof of Theorem 15.3.2
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0007
Copyright Page
(2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.002.0003
Explicit examples of GFT tensor Feynman integral computations
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0004
Coherent states ofSU(2)
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0005
Examples of tree weights
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0001
TheB+ operator in Moyal QFT, two-loop examples
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0003
Proof of Theorem 16.1.1
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0008
Renormalization of the Grosse–Wulkenhaar model, one-loop examples
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0002
Dedication
(2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.002.0004
Proof of the double-scaling limit of theU(N)D-invariant tensor model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0006
Summary of results on the diagrammatics of the coloured SYK model and of the Gurău–Witten model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0009
A direct approach to coherent states of billiards using a quantum algebra framework
Maioli, A. C., & Curado, E. M. F. (2025) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887825400328

Authors: Witten, E.
Affiliations: Princeton University (US)
Corresponding author: Witten, Edward
ORCID: Witten, Edward
Venue: Nuclear Physics B
Publisher: Elsevier BV
Published: 1990-01
Volume: 330
Issue: 2-3
Pages: 285-346
ISSN: 0550-3213 (ISSN-L)
DOI: 10.1016/0550-3213(90)90115-t
OpenAlex: W1968829869
Cited by: 278
References: 29
Citations by year: 2025: 5 · 2023: 2 · 2022: 1 · 2021: 30 · 2019: 6 · 2018: 5 · 2017: 5 · 2016: 4 · 2015: 5 · 2014: 2 · 2013: 6 · 2012: 4
FWCI: 42.66
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Nuclear Physics B (publishedVersion)
Topics: Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords: Jones polynomial, vertex model, quantum groups, Chern-Simons theory, gauge theory, knot invariants, integrable systems, statistical mechanics, duality, three-dimensional gauge theory

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Gauge theories, vertex models, and quantum groups

Overview

Integrity signals

Verification

Claims the paper makes

Citations

Cites

Cited by

Related

Metadata

Record

About these checks