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Irreducible Representations of Quantum Affine Algebras

Thorén, Jesper LU (2000)
Abstract
We construct finite-dimensional representations of the quantum affine algebra associated to the simple finite-dimensional Lie algebra sl(n+1). The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. To do this, we find a particular basis of every fundamental representation, consisting of eigenvectors for some of the Drinfeld generators of the algebra. The tensor product of such basis vectors are also eigenvectors, and this simplifies the study of the modules.



We consider the trigonometric solutions of the quantum Yang-Baxter equation with spectral parameters associated to the irreducible finite-dimensional representations of the quantum affine... (More)
We construct finite-dimensional representations of the quantum affine algebra associated to the simple finite-dimensional Lie algebra sl(n+1). The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. To do this, we find a particular basis of every fundamental representation, consisting of eigenvectors for some of the Drinfeld generators of the algebra. The tensor product of such basis vectors are also eigenvectors, and this simplifies the study of the modules.



We consider the trigonometric solutions of the quantum Yang-Baxter equation with spectral parameters associated to the irreducible finite-dimensional representations of the quantum affine algebra associated to sl(2), using some earlier results.



The explicit comultiplication of the Drinfeld generators is found in the sl(2)-case by solving a functional equation induced by the defining relations in the quantum affine algebra. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Prof. Cox, Ben, University of Charleston
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Number Theory, Matematik, Mathematics, quantum evaluation modules, highest weight representations, quantum Yang-Baxter equation, quantum affine algebras, quantum groups, comultiplication, Hopf algebras, affine Lie algebras, field theory, algebraic geometry, algebra, group theory, Talteori, fältteori, algebraisk geometri, gruppteori
pages
134 pages
defense location
Sal C Matematikhuset
defense date
2000-05-13 13:15
external identifiers
  • Other:ISRN: LUNFMA-1013-2000
ISSN
1404-0034
ISBN
91-628-4152-1
language
English
LU publication?
yes
id
31297e6a-99c4-4c87-9e1b-4ffe0d1033ef (old id 19637)
date added to LUP
2007-05-25 15:49:56
date last changed
2016-09-19 08:45:00
@phdthesis{31297e6a-99c4-4c87-9e1b-4ffe0d1033ef,
  abstract     = {We construct finite-dimensional representations of the quantum affine algebra associated to the simple finite-dimensional Lie algebra sl(n+1). The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. To do this, we find a particular basis of every fundamental representation, consisting of eigenvectors for some of the Drinfeld generators of the algebra. The tensor product of such basis vectors are also eigenvectors, and this simplifies the study of the modules.<br/><br>
<br/><br>
We consider the trigonometric solutions of the quantum Yang-Baxter equation with spectral parameters associated to the irreducible finite-dimensional representations of the quantum affine algebra associated to sl(2), using some earlier results.<br/><br>
<br/><br>
The explicit comultiplication of the Drinfeld generators is found in the sl(2)-case by solving a functional equation induced by the defining relations in the quantum affine algebra.},
  author       = {Thorén, Jesper},
  isbn         = {91-628-4152-1},
  issn         = {1404-0034},
  keyword      = {Number Theory,Matematik,Mathematics,quantum evaluation modules,highest weight representations,quantum Yang-Baxter equation,quantum affine algebras,quantum groups,comultiplication,Hopf algebras,affine Lie algebras,field theory,algebraic geometry,algebra,group theory,Talteori,fältteori,algebraisk geometri,gruppteori},
  language     = {eng},
  pages        = {134},
  school       = {Lund University},
  title        = {Irreducible Representations of Quantum Affine Algebras},
  year         = {2000},
}