(ZN×)n-1 generalization of the chiral Potts model

V. V. Bazhanov; R. M. Kashaev; V. V. Mangazeev; Yu G. Stroganov

doi:10.1007/BF02099497

(Z_N×)^n-1 generalization of the chiral Potts model

V. V. Bazhanov^*, R. M. Kashaev, V. V. Mangazeev, Yu G. Stroganov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

87 Citations (Scopus)

Abstract

We show that the R-matrix which intertwines two n-by-N^n-1 state cyclic L-operators related with a generalization of U_q(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g=N^{2(n-1)((n-1)N-n)+1} defined by 2 n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.

Original language	English
Pages (from-to)	393-408
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	138
Issue number	2
DOIs	https://doi.org/10.1007/BF02099497
Publication status	Published - May 1991
Externally published	Yes

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abstract = "We show that the R-matrix which intertwines two n-by-Nn-1 state cyclic L-operators related with a generalization of Uq(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g=N2(n-1)((n-1)N-n)+1 defined by 2 n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.",

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AU - Bazhanov, V. V.

AU - Kashaev, R. M.

AU - Mangazeev, V. V.

AU - Stroganov, Yu G.

PY - 1991/5

Y1 - 1991/5

N2 - We show that the R-matrix which intertwines two n-by-Nn-1 state cyclic L-operators related with a generalization of Uq(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g=N2(n-1)((n-1)N-n)+1 defined by 2 n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.

AB - We show that the R-matrix which intertwines two n-by-Nn-1 state cyclic L-operators related with a generalization of Uq(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g=N2(n-1)((n-1)N-n)+1 defined by 2 n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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ER -

(Z_N×)^n-1 generalization of the chiral Potts model

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