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 $\mathfrak{sl}^N$, 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
Review in the context of AdS-CFT includes
In
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.