Irreducible Representations of Quantum Affine Algebras

Jesper Thorén

Research output: ThesisDoctoral Thesis (monograph)

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 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.
Original languageEnglish
QualificationDoctor
Awarding Institution
  • Mathematics (Faculty of Sciences)
Supervisors/Advisors
  • [unknown], [unknown], Supervisor, External person
Award date2000 May 13
ISBN (Print)91-628-4152-1
Publication statusPublished - 2000

Bibliographical note

Defence details

Date: 2000-05-13
Time: 13:15
Place: Sal C Matematikhuset

External reviewer(s)

Name: Cox, Ben
Title: Prof.
Affiliation: University of Charleston

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Subject classification (UKÄ)

  • Mathematics

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

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