Eigenvectors in the Superintegrable Model I: sl_2 Generators

Abstract

In order to calculate correlation functions of the chiral Potts model, one only needs to study the eigenvectors of the superintegrable model. Here we start this study by looking for eigenvectors of the transfer matrix of the periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is 2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N. We introduce chiral Potts model operators, different from the more commonly used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form the generators of a loop algebra L(sl(2)). For this algebra, we then use the roots of the Drinfeld polynomial to give new explicit expressions for the generators representing the loop algebra as the direct sum of r copies of the simple algebra sl(2).

LaTeX 2E document, 11 pages, 1 eps figure, using iopart.cls with graphicx and iopams packages. v2: Appended text to title, added acknowledgments and made several minor corrections v3: Added reference, eliminated ambiguity, corrected a few misprints

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Cited by in corpus (19)

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• 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
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Eigenvectors in the Superintegrable Model II: Ground State Sector
• Polynomial Triangles Revisited
• Factorized finite-size Ising model spin matrix elements from Separation of Variables
• Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ
• Identities in the Superintegrable Chiral Potts Model
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
• On ${\tau }^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(s{l}_2)$
• Spontaneous Magnetization of the Integrable Chiral Potts Model
• Serre Relations in the Superintegrable 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
• Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths
• Duality and Symmetry in Chiral Potts Model