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Quantum Loop Algebras, Yangians and their Representations

  • Author / Creator
    Conner, Patrick M
  • 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.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3KS6JB4C
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Guay, Nicolas (Mathematics)
  • Examining committee members and their departments
    • Gannon, Terry (Mathematics)
    • Cliff, Gerald (Mathematics)
    • Guay, Nicolas (Mathematics)
    • Berger, Arno (Mathematics)