Irreducible Representations of Quantum Affine Algebras
Research output: Thesis › Doctoral Thesis (monograph)
Abstract
We construct finitedimensional representations of the quantum affine algebra associated to the simple finitedimensional 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 YangBaxter equation with spectral parameters associated to the irreducible finitedimensional 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.
We consider the trigonometric solutions of the quantum YangBaxter equation with spectral parameters associated to the irreducible finitedimensional 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.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Qualification  Doctor 
Awarding Institution  
Supervisors/Assistant supervisor 

Award date  2000 May 13 
Print ISBNs  9162841521 
Publication status  Published  2000 
Publication category  Research 
Bibliographic note
Defence details
Date: 20000513
Time: 13:15
Place: Sal C Matematikhuset
External reviewer(s)
Name: Cox, Ben
Title: Prof.
Affiliation: University of Charleston
