### Abstract

An elliptic deformation of {Mathematical expression} is proposed. Our presentation of the algebra is based on the relation RLL = LLR^{*}, where R and R^{*} are eight-vertex R-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation of R^{*} is discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 259-268 |

Number of pages | 10 |

Journal | Letters in Mathematical Physics |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1 1994 |

Externally published | Yes |

### Fingerprint

### Keywords

- Mathematics Subject Classifications (1991): 17B37, 82A67

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

_{2}- Dedicated to the memory of Ansgar Schnizer.

*Letters in Mathematical Physics*,

*32*(3), 259-268. https://doi.org/10.1007/BF00750668

**An elliptic quantum algebra for {Mathematical expression} _{2} - Dedicated to the memory of Ansgar Schnizer.** / Foda, Omar; Iohara, Kenji; Jimbo, Michio; Kedem, Rinat; Miwa, Tetsuji; Yan, Hong.

Research output: Contribution to journal › Article

_{2}- Dedicated to the memory of Ansgar Schnizer',

*Letters in Mathematical Physics*, vol. 32, no. 3, pp. 259-268. https://doi.org/10.1007/BF00750668

_{2}- Dedicated to the memory of Ansgar Schnizer. Letters in Mathematical Physics. 1994 Nov 1;32(3):259-268. https://doi.org/10.1007/BF00750668

}

TY - JOUR

T1 - An elliptic quantum algebra for {Mathematical expression}2 - Dedicated to the memory of Ansgar Schnizer

AU - Foda, Omar

AU - Iohara, Kenji

AU - Jimbo, Michio

AU - Kedem, Rinat

AU - Miwa, Tetsuji

AU - Yan, Hong

PY - 1994/11/1

Y1 - 1994/11/1

N2 - An elliptic deformation of {Mathematical expression} is proposed. Our presentation of the algebra is based on the relation RLL = LLR*, where R and R* are eight-vertex R-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation of R* is discussed.

AB - An elliptic deformation of {Mathematical expression} is proposed. Our presentation of the algebra is based on the relation RLL = LLR*, where R and R* are eight-vertex R-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation of R* is discussed.

KW - Mathematics Subject Classifications (1991): 17B37, 82A67

UR - http://www.scopus.com/inward/record.url?scp=0001503127&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001503127&partnerID=8YFLogxK

U2 - 10.1007/BF00750668

DO - 10.1007/BF00750668

M3 - Article

AN - SCOPUS:0001503127

VL - 32

SP - 259

EP - 268

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

ER -