nLab Yangian




A Yangian is a certain quantum group that arises naturally in integrable systems in quantum field theory, as well as in semi-holomorphic 4d Chern-Simons theory.


  • Wikipedia, Yangian

  • A. I. Molev, Yangians and their applications, in “Handbook of Algebra” vol. 3 (M. Hazewinkel, Ed.), Elsevier 2003, 907-959 math.QA/0211288

  • A. I. Molev, Yangians and classical Lie algebras, AMS Math. Surv. Monog. 143, 2007; 400 pp; Russian edition: Янгианы и классические алгебры Ли, МЦНМО, Москва, 2009

  • N. J. Mackay, Introduction to Yangian symmetry in integrable field theory (arXiv:hep-th/0409183)

  • Vassili Gorbounov, R. Rimanyi, V. Tarasov, A. Varchenko, Cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra, arXiv:1204.5138

  • V. G. Drinfeld, Degenerate affine Hecke algebras and Yangians, Funct. Anal. Appl. 20 (1986), 58–60.

  • Denis Uglov, Symmetric functions and the Yangian decomposition of the Fock and basic modules of the affine Lie algebra 𝔰𝔩 N\mathfrak{sl}^N, Math. Soc. Japan Memoirs 1, 1998, 183-241 euclid doi

  • A. N. Kirillov, N. Y. Reshetikhin, The Yangians, Bethe Ansatz and combinatorics, Lett. Math. Phys. 12, 199 (1986)

  • Sachin Gautam, Valerio Toledano-Laredo, Yangians and quantum loop algebras, Selecta Mathematica 19 (2013), 271-336 arxiv/1012.3687; II. Equivalence of categories via abelian difference equations arxiv/1310.7318; III. Meromorphic equivalence of tensor structures arxiv/1403.5251

Yangians for quivers and relation to quantum equivariant cohomology of Nakajima’s quiver varieties

  • Davesh Maulik, Andrei Okounkov, Quantum groups and quantum cohomology, Astérisque 408, SMF 2019 arXiv:1211.1287

Review in the context of AdS-CFT includes


is discussed that the holomorphically twisted N=1 D=4 super Yang-Mills theory is controled by the Yangian in analogy to how Chern-Simons theory is controled by a quantum group. See at semi-holomorphic 4d Chern-Simons theory.

Last revised on October 12, 2022 at 11:14:58. See the history of this page for a list of all contributions to it.