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 journalArticle

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 languageEnglish (US)
Pages (from-to)259-268
Number of pages10
JournalLetters in Mathematical Physics
Volume32
Issue number3
DOIs
StatePublished - Nov 1 1994
Externally publishedYes

Fingerprint

Quantum Algebra
algebra
apexes
Vertex Operators
Algebra
quotients
R-matrix
Modulus
Quotient
modules
operators
Module
Vertex of a graph
Presentation
Interpretation

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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.

In: Letters in Mathematical Physics, Vol. 32, No. 3, 01.11.1994, p. 259-268.

Research output: Contribution to journalArticle

Foda, Omar ; Iohara, Kenji ; Jimbo, Michio ; Kedem, Rinat ; Miwa, Tetsuji ; Yan, Hong. / An elliptic quantum algebra for {Mathematical expression}2 - Dedicated to the memory of Ansgar Schnizer. In: Letters in Mathematical Physics. 1994 ; Vol. 32, No. 3. pp. 259-268.
@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 = "11",
day = "1",
doi = "10.1007/BF00750668",
language = "English (US)",
volume = "32",
pages = "259--268",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Netherlands",
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 - 1994/11/1

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 -