sl(N) Onsager's Algebra and Integrability

Abstract

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion.

References in corpus (1)

• Physics beyond quasi-particles: Spectrum and completeness of the 3 state superintegrable chiral Potts model

Cited by in corpus (30)

• Deformed Dolan-Grady relations in quantum integrable models
• Integrable Floquet dynamics
• The structure of quotients of the Onsager algebra by closed ideals
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Some algebra related to $P$-and $Q$-polynomial association schemes
• The Askey-Wilson algebra and its avatars
• Generalised Onsager Algebra in Quantum Lattice Models
• Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
• Finite-dimensional irreducible modules for the three-point ${\mathfrak{sl}}_2$ loop algebra
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• Dynamical Correlation Functions and Finite-size Scaling in Ruijsenaars-Schneider Model
• Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations
• The algebraic structure of the Onsager algebra
• FRT presentation of the Onsager algebras
• Generalized q-Onsager algebras and boundary affine Toda field theories
• Onsager algebra and algebraic generalization of Jordan-Wigner transformation
• Vertex Ring-Indexed Lie Algebras
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Quantum spin chains from Onsager algebras and reflection $K$-matrices
• The $q$-tetrahedron algebra and its finite dimensional irreducible modules
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Generalized Onsager algebras
• Higher order relations for ADE-type generalized q-Onsager algebras
• The higher order $q$-Dolan-Grady relations and quantum integrable systems
• Polynomially restricted operator growth in dynamically integrable models
• Extension of a Borel subalgebra symmetry into the sl(2) loop algebra symmetry for the twisted XXZ spin chain at roots of unity and the Onsager algebra
• The Onsager Algebra
• Conserved Charges of Series of Solvable Lattice Models
• Matrix equations and trilinear commutation relations
• Parity anomaly from LSM: exact valley symmetries on the lattice