Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials

M. Jimbo, R. Kedem, H. Konno, T. Miwa, J. U.H. Petersen

Research output: Contribution to journalArticle

Abstract

The level-1 integrable highest weight modules of Uq(sl 2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-1 module generated by components of vertex operators. Each level-1 module is a direct sum of finite-dimensional irreducible level-0 modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-1 modules.

Original languageEnglish (US)
Article number014
Pages (from-to)5589-5606
Number of pages18
JournalJournal of Physics A: Mathematical and General
Volume28
Issue number19
DOIs
StatePublished - Dec 1 1995
Externally publishedYes

Fingerprint

Macdonald Polynomials
Algebra
polynomials
modules
Polynomials
Module
Decomposition
algebra
Affine Hecke Algebra
Character Formula
Vertex Operators
Direct Sum
apexes
Decompose
decomposition
operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials. / Jimbo, M.; Kedem, R.; Konno, H.; Miwa, T.; Petersen, J. U.H.

In: Journal of Physics A: Mathematical and General, Vol. 28, No. 19, 014, 01.12.1995, p. 5589-5606.

Research output: Contribution to journalArticle

Jimbo, M. ; Kedem, R. ; Konno, H. ; Miwa, T. ; Petersen, J. U.H. / Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials. In: Journal of Physics A: Mathematical and General. 1995 ; Vol. 28, No. 19. pp. 5589-5606.
@article{d2d0c533f1ec4437b83d6cab467155f5,
title = "Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials",
abstract = "The level-1 integrable highest weight modules of Uq(sl 2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-1 module generated by components of vertex operators. Each level-1 module is a direct sum of finite-dimensional irreducible level-0 modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-1 modules.",
author = "M. Jimbo and R. Kedem and H. Konno and T. Miwa and Petersen, {J. U.H.}",
year = "1995",
month = "12",
day = "1",
doi = "10.1088/0305-4470/28/19/014",
language = "English (US)",
volume = "28",
pages = "5589--5606",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "19",

}

TY - JOUR

T1 - Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials

AU - Jimbo, M.

AU - Kedem, R.

AU - Konno, H.

AU - Miwa, T.

AU - Petersen, J. U.H.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - The level-1 integrable highest weight modules of Uq(sl 2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-1 module generated by components of vertex operators. Each level-1 module is a direct sum of finite-dimensional irreducible level-0 modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-1 modules.

AB - The level-1 integrable highest weight modules of Uq(sl 2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-1 module generated by components of vertex operators. Each level-1 module is a direct sum of finite-dimensional irreducible level-0 modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-1 modules.

UR - http://www.scopus.com/inward/record.url?scp=0347208803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347208803&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/19/014

DO - 10.1088/0305-4470/28/19/014

M3 - Article

AN - SCOPUS:0347208803

VL - 28

SP - 5589

EP - 5606

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 19

M1 - 014

ER -