Irreducible Representations of Quantum Affine Algebras
(2000) 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... (More)  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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/19637
 author
 Thorén, Jesper ^{LU}
 supervisor
 opponent

 Prof. Cox, Ben, University of Charleston
 organization
 publishing date
 2000
 type
 Thesis
 publication status
 published
 subject
 keywords
 Number Theory, Matematik, Mathematics, quantum evaluation modules, highest weight representations, quantum YangBaxter 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
 20000513 13:15
 external identifiers

 other:ISRN: LUNFMA10132000
 ISSN
 14040034
 ISBN
 9162841521
 language
 English
 LU publication?
 yes
 id
 31297e6a99c44c879e1b4ffe0d1033ef (old id 19637)
 date added to LUP
 20070525 15:49:56
 date last changed
 20180529 09:41:24
@phdthesis{31297e6a99c44c879e1b4ffe0d1033ef, 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.<br/><br> <br/><br> 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.<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 = {9162841521}, issn = {14040034}, keyword = {Number Theory,Matematik,Mathematics,quantum evaluation modules,highest weight representations,quantum YangBaxter 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}, }