Yangians, quantum loop algebras, and abelian difference equations

DOI10.1090/jams/851zbMath1336.17012arXiv1310.7318OpenAlexW2963625711MaRDI QIDQ2802071

Valerio Toledano Laredo, Sachin Gautam

Publication date: 25 April 2016

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.7318

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Additive difference equations (39A10) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Related Items (17)

Elliptic quantum groups and Baxter relations ⋮ Meromorphic tensor equivalence for Yangians and quantum loop algebras ⋮ Asymptotic representations of quantum affine superalgebras ⋮ Baxter operators and asymptotic representations ⋮ Length-two representations of quantum affine superalgebras and Baxter operators ⋮ Baxter's relations and spectra of quantum integrable models ⋮ Yangians and Baxter's relations ⋮ An explicit isomorphism between quantum and classical \(\mathfrak{sl}_n \) ⋮ The PBW theorem for affine Yangians ⋮ Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra ⋮ Equivalences between three presentations of orthogonal and symplectic Yangians ⋮ The \(R\)-matrix presentation for the Yangian of a simple Lie algebra ⋮ Coproduct for Yangians of affine Kac-Moody algebras ⋮ Isomorphism of the Yangian \(Y_{\hbar}(A(m, n))\) of the special linear Lie superalgebra and the quantum loop superalgebra \(U_{\hbar}(LA(m, n))\) ⋮ Vertex representations for Yangians of Kac-Moody algebras ⋮ The meromorphic \(R\)-matrix of the Yangian ⋮ Poles of finite-dimensional representations of Yangians

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