Algebraic Structures Related to Reflection Equations

Abstract

Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations, real forms, fusion procedure etc) as well as the generalizations are discussed.

18 pages

Cited by in corpus (82)

• Quantum symmetric Kac-Moody pairs
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Correlation functions of the open XXZ chain I
• Deformed Dolan-Grady relations in quantum integrable models
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Correlation functions of the open XXZ chain II
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Finite-dimensional irreducible representations of twisted Yangians
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Reflection K-Matrices for 19-Vertex Models
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities
• Bethe Ansatz and Q-operator for the open ASEP
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• Baxterized Solutions of Reflection Equation and Integrable Chain Models
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Reflection equations and q-Minkowski space algebras
• Classical integrable systems and soliton equations related to eleven-vertex R-matrix
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Tetrahedron and 3D reflection equations from quantized algebra of functions
• Universal K-matrices for quantum Kac-Moody algebras
• Characteristic Relations for Quantum Matrices
• On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Set-theoretical reflection equation: Classification of reflection maps
• Solutions of the boundary Yang-Baxter equation for arbitrary spin
• Spectral extension of the quantum group cotangent bundle
• On reflection algebras and twisted Yangians
• On the physical contents of q-deformed Minkowski spaces
• Introduction to Quantum Integrability
• Comodule algebras and integrable systems
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• A quantum algebraic description of D-branes on group manifolds
• Quantum Groups, $q$-Oscillators and Covariant Algebras
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• Baxterization of solutions to reflection equation with Hecke R-matrix
• New boundary conditions for integrable lattices
• Trigonometric sl(2) Gaudin model with boundary terms
• Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems
• Deformed Minkowski spaces: clasification and properties
• On the algebraic structure of differential calculus on quantum groups
• Non-Levi closed conjugacy classes of SP_q(2n)
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion
• Weyl approach to representation theory of reflection equation algebra
• A new dynamical reflection algebra and related quantum integrable systems
• A Q-operator for open spin chains I: Baxter's TQ relation
• Commuting quantum traces for quadratic algebras
• Jordanian deformation of the open XXX-spin chain
• Double quantization of $\cp$ type orbits by generalized Verma modules
• Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis
• Quantum Supersymmetric Toda-mKdV Hierarchies
• Unrestricted Quantum Moduli Algebras. I. The Case of Punctured Spheres
• Solutions of the $U_q({\widehat{\mathfrak{sl}}}_N)$ reflection equations
• The Kondo effect in the quantum $XX$ spin chain
• Quantum current algebras associated with rational $R$-matrix
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Quasi modules for the quantum affine vertex algebra in type $A$
• Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Cayley-Hamilton Theorem for Symplectic Quantum Matrix Algebras
• Quantization of the N=2 Supersymmetric KdV Hierarchy
• Reflection equation and twisted Yangians
• Coadditive differential complexes on quantum groups and quantum spaces
• Tensor K-matrices for quantum symmetric pairs
• The Prime Spectrum and Representation Theory of the $2\times 2$ Reflection Equation Algebra
• Diagonal solutions to reflection equations in higher spin XXZ model
• Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials
• Jordanian deformation of the open sl(2) Gaudin model
• Non-commutative geometry and covariance: from the quantum plane to the quantum tensors
• Equivariant vector bundles over quantum projective spaces
• On construction of unitary quantum group differential calculus
• Quantum Matrix Models for Simple Current Orbifolds
• Brane Bulk Couplings and Condensation from REA Fusion
• Twisted WZW Branes from Twisted REA's
• Boundary transfer matrices arising from quantum symmetric pairs
• Isomorphisms between Quantum Group Covariant q-Oscillator Systems Defined for q and 1/q
• A quantum homogeneous space of nilpotent matrices
• Scattering matrices in the sl(3) twisted Yangian
• Freidel-Maillet type presentations of $U_q(s{l}_2)$
• BC-type open $SL(2,\mathbb{C})$ spin chain
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish