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Irreducible representation, Quantum loop algebra, Degenerate form, Yangian

Conner, Patrick M

Supervisor and department: Guay, Nicolas Mathematics

Examining committee member and department: Berger, Arno Mathematics Cliff, Gerald Mathematics Guay, Nicolas Mathematics Gannon, Terry Mathematics

Department: Department of Mathematical and Statistical Sciences

Specialization: Mathematics

Date accepted: 2014-08-27T10:39:19Z

Graduation date: 2014-11

Degree: Master of Science

Degree level: Master's

Abstract: Among representation theorists, it is well known that Yangians can be realized as some type of degenerate form of quantum loop algebras. What is not well known is precisely how this degeneration takes place. In the first part of this thesis, we will demonstrate explicitly the process by which certain quantum loop algebras degenerate into an associated Yangian. In the second part, we will prove a theorem which classifies all of the finite dimensional irreducible representations of Yangians over complex semisimple Lie algebras.

Language: English

DOI: doi:10.7939-R3KS6JB4C

Rights: Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.

Autor: Conner, Patrick M

Fuente: https://era.library.ualberta.ca/


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