The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model

Abstract

The loop algebra $L({\mathfrak{sl}}_2)$ symmetry is found in a sector of the nilpotent Bazhanov-Stroganov model. The Drinfeld polynomial of a $L({\mathfrak{sl}}_2)$-degenerate eigenspace of the model is equivalent to the polynomial which characterizes a subspace with the Ising-like spectrum of the superintegrable chiral Potts model.

arXiv comment8 pages, to be published in Phys. Lett. A

References in corpus (4)

• Quantum Inverse Scattering Method and Correlation Functions
• Bethe's equation is incomplete for the XXZ model at roots of unity
• Physics beyond quasi-particles: Spectrum and completeness of the 3 state superintegrable chiral Potts model
• The algebraic structure of the Onsager algebra

Cited by in corpus (24)

• Onsager symmetries in $U(1)$-invariant clock models
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model
• Eigenvectors in the Superintegrable Model I: sl_2 Generators
• Spin operator matrix elements in the quantum Ising chain: fermion approach
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• Some remarks on a generalization of the superintegrable chiral Potts model
• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
• Eigenvectors in the Superintegrable Model II: Ground State Sector
• Finite-dimensional irreducible modules for the three-point ${\mathfrak{sl}}_2$ loop algebra
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• Identities in the Superintegrable Chiral Potts Model
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• Spontaneous Magnetization of the Integrable Chiral Potts Model
• On ${\tau }^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(s{l}_2)$
• Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
• Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
• Analogues of Lusztig's higher order relations for the q-Onsager algebra
• Serre Relations in the Superintegrable Model
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Duality and Symmetry in Chiral Potts Model
• 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