Yangians and classical Lie algebras

DOI10.1070/RM1996v051n02ABEH002772zbMath0876.17014arXivhep-th/9409025OpenAlexW2953337841MaRDI QIDQ4341899

Grigori Olshanski, M. L. Nazarov, Alexander I. Molev

Publication date: 30 June 1997

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9409025

zbMATH Keywords

filtration bibliography center Yang-Baxter equation Yangians Hopf algebra antipode $R$-matrix block matrices involutory automorphism Poincaré-Birkhoff-Witt theorem Sklyanin determinant quantum determinant twisted Yangian polynomial current Lie algebra quantum contraction quantum Liouville formula

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) Hopf algebras and their applications (16T05) Yang-Baxter equations (16T25)

Related Items

Polygon gluing and commuting bosonic operators, A note on the center of the super Yangian $Y_{M|N}(\mathfrak{s})$, A note on constructing quasi modules for quantum vertex algebras from twisted Yangians, From braces to Hecke algebras and quantum groups, The centre of the modular super Yangian Ym|n$Y_{m|n}$, The centralizer construction and Yangian-type algebras, Representations of twisted Yangians of types B, C, D: I, (Quantum) twisted Yangians: Symmetry, Baxterisation, and centralizers, Unnamed Item, Exactly solvable models in atomic and molecular physics, Conformal algebra: R-matrix and star-triangle relation, Algebraic properties of Manin matrices. I, Twisted Yangians, Drinfeld approach, Yangian-type symmetries of non-planar leading singularities, Truncation of the reflection algebra and the Hahn algebra, Two determinants in the universal enveloping algebras of the orthogonal Lie algebras, The quantum super-Yangian and Casimir operators of $U_ q{\mathfrak {gl}}(M| N)$, Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems, Twisted Yangians for symmetric pairs of types B, C, D, Yangian symmetry for bi-scalar loop amplitudes, COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS, Verma modules for Yangians, On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains, R -matrix presentation for super-Yangians Y(osp(m|2n)), Twisted super-Yangians and their representations, On Bethe vectors in $ \mathfrak{g}{\mathfrak{l}}_3 $-invariant integrable models, Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra, An analysis of the multiplicity spaces in branching of symplectic groups., Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras, Irreducibility of fusion modules over twisted Yangians at generic point, A new dynamical reflection algebra and related quantum integrable systems, The Yangian of the strange Lie superalgebra and its quantum double, Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation, More on affine Dynkin quiver Yangians, Spectral theory of the Nazarov-Sklyanin Lax operator, Shuffle algebra realizations of type $A$ super Yangians and quantum affine superalgebras for all Cartan data, Integrable crosscap states in $\mathfrak{gl}(N)$ spin chains, Classification of reflection matrices related to (super-)Yangians and application to open spin chain models, Rational representations of the Yangian $\text Y(\mathfrak {gl}_n)$, $q$-Poincaré supersymmetry in $\text{AdS}_5/\text{CFT}_4$, Coideal algebras from twisted Manin triples, Yangian symmetric correlators, Parabolic presentations of the super Yangian ${Y(\mathfrak{gl}_{M|N})}$, Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory, Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra, Yangian of the general linear Lie superalgebra, Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry, Reflection equation and twisted Yangians, Representation theory of rectangular finite $W$-algebras, Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries, Generalized Bell states and principal realization of the Yangian $Y(\mathfrak {sl}_{N})$Y(slN), Bethe vectors ofGL(3)-invariant integrable models, Integrable approach to simple exclusion processes with boundaries. Review and progress, Scattering matrices in the $\mathfrak{sl}({\mbox{\sffamily\bfseries 3}})$ twisted Yangian, Manin matrices for quadratic algebras, Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type $BC$, Gauss decomposition of the Yangian $Y({\mathfrak{gl}}_{m|n})$, TWISTED YANGIANS AND FOLDED ${\mathcal W}$ -ALGEBRAS, Drinfeld J presentation of twisted Yangians, Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an $\mathrm{SL}(n,\mathbb{C})$-invariant spin chain, Principal realization of twisted Yangian ${Y(\mathfrak{g}_{N})}$, Twisted Yangians and Mickelsson Algebras. II, Separation of variables for the quantum $\mathrm{SL} (3, \mathbb{C} )$ spin magnet: eigenfunctions of the Sklyanin $B$-operator, On a class of representations of the Yangian and moduli space of monopoles, A Cayley-Hamilton theorem for the skew Capelli elements, Analytical Bethe ansatz in $\text{gl}(N)$ spin chains, Photon-added coherent states for the Morse oscillator, Gelfand–Tsetlin Bases for Classical Lie Algebras, REPRESENTATIONS OF REFLECTION ALGEBRAS, Schubert calculus and representations of the general linear group, The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz, Twisted Yangians of small rank, Yangian symmetry of string theory on $\mathrm{AdS}_{3} \times S^{3} \times S^{3} \times S^{1}$ with mixed 3-form flux, On the freeness problem for truncated current algebras, Parabolic presentations of the super Yangian $Y(\mathfrak{gl}_{M|N})$ associated with arbitrary 01-sequences, Finite-dimensional irreducible representations of twisted Yangians, ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES, Analytical Bethe ansatz for closed and opengl(Script N)-spin chains in any representation, Gelfand-Tsetlin degeneration of shift of argument subalgebras in types B, C and D, ANALYTICAL BETHE ANSATZ FOR OPEN SPIN CHAINS WITH SOLITON NONPRESERVING BOUNDARY CONDITIONS, Gelfand–Tsetlin varieties for 𝔤𝔩n, Double Yangian and the universal $R$-matrix, Grigori Iosifovich Olshanski, Explicit Newton's formula for ${\mathfrak gl}_n$, Gauge theory and boundary integrability, Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices, Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra, Yangian symmetry in integrable quantum gravity, Yangian and topological basis expressions of two types of XXZ spin chains, Bethe eigenvectors of higher transfer matrices, The thermodynamical limit of generalgl(N) spin chains: the vacuum state and densities, Gauge theory and boundary integrability. II: Elliptic and trigonometric cases, The quantum determinant of the elliptic algebra $ {\mathcal{A}_{q, p}(\mathfrak{\widehat{gl}}_N)}$, On Turnbull identity for skew-symmetric matrices, On boundary superalgebras, Parabolic presentations of the Yangian $Y(\mathfrak{gl}_n)$, Monodromy bootstrap for $\mathrm{SU}(2|2)$ quantum spectral curves: from Hubbard model to $\mathrm{AdS}_3/\mathrm{CFT}_2$, Irreducibility criterion for tensor products of Yangian evaluation modules., $R$-matrix realization of two-parameter quantum group $U_{r,s}(\mathfrak {gl}_n)$, Symmetry properties of Wilson loops with a Lagrangian insertion, On reflection algebras and twisted Yangians, Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system, The Askey–Wilson algebra and its avatars, Representations of classical Lie groups and quantized free convolution, Shifted Yangians and finite $W$-algebras