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
A. Molev, M. Nazarov, G. Ol’shanskii, Yangians and classical Lie algebras, Russian Mathematical Surveys 51(2) (1996) 205–282 doi
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; Yangians, quantum loop algebras and abelian difference equations (Formerly: Yangians and quantum loop algebras II. Equivalence of categories via abelian difference equations) J. Amer. Math. Soc. 29 (2016) 775–824 arXiv:1310.7318; III. Meromorphic tensor equivalence for Yangians and quantum loop algebras, Publ.math. IHES 125, 267–337 (2017). doi arXiv:1403.5251
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov, Towards the theory of Yangians [arXiv:2311.00760]
Braided Yangians and Yangians associated to R-matrices:
Yangians for quivers and relation to quantum equivariant cohomology of Nakajima’s quiver varieties:
Review in the context of AdS-CFT includes
Quiver Yangians appearing in description of Hall algebras of $\omega$-semistable compactly supported sheaves with fixed slope on resolutions of Kleinian singularities:
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 September 29, 2024 at 10:38:41. See the history of this page for a list of all contributions to it.