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

Omar Foda; Kenji Iohara; Michio Jimbo; Rinat Kedem; Tetsuji Miwa; Hong Yan

doi:10.1007/BF00750668

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

Omar Foda, Kenji Iohara, Michio Jimbo, Rinat Kedem, Tetsuji Miwa, Hong Yan

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

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	https://doi.org/10.1007/BF00750668
State	Published - Nov 1994
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Online availability

10.1007/BF00750668

Library availability

Discover UIUC Full Text

Cite this

@article{5c313277e03f45bfa9889d90a9b2cc3c,

title = "An elliptic quantum algebra for {Mathematical expression}2 - Dedicated to the memory of Ansgar Schnizer",

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.",

keywords = "Mathematics Subject Classifications (1991): 17B37, 82A67",

author = "Omar Foda and Kenji Iohara and Michio Jimbo and Rinat Kedem and Tetsuji Miwa and Hong Yan",

year = "1994",

month = nov,

doi = "10.1007/BF00750668",

language = "English (US)",

volume = "32",

pages = "259--268",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer",

number = "3",

}

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

Y1 - 1994/11

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 -