Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

Abstract

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.

LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introduction

References in corpus (4)

• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model
• Identities in the Superintegrable Chiral Potts Model
• Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations

Cited by in corpus (5)

• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Parafermions in the tau-2 model
• Spin operator matrix elements in the quantum Ising chain: fermion approach
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• Analogues of Lusztig's higher order relations for the q-Onsager algebra